i've been trying to crack functions and this video made it so so easy. I woke up this morning not knowing how to do the function questions, and will go to bed knowing exactly how to tackle them. thank you!
I tried solving question 5 both algebraically and by picking up numbers for a, b and c and it turned out that picking up numbers is particularly quicker especially on statement 3.
I do wish I could see the algebra for the symbol question, because it wasn't working out for me when I tried running through it with pen and paper. Not really that important, though, because I couldn't really take that approach on the test.
hey, in that triangle problem can we cancel x from both sides of defined equation so that we get the equation in only y form ?, it gets same -1 result.
Did you divide by x on both sides and get 1 triangle y = 2(y^2) ? If so, essentially what you're doing is substituting '1' in for 'x'. How did you actually do the step with -4 triangle 2 ? I "think" you can get away with that canceling here based on how this particular function has been defined. But it's not a shortcut I'd employ on function problems universally in the future.
Hey Jeff question on the last one. I see that you assumed the nested f(x) function equals 82 because that’s what stated in the problem stem. However there is ambiguity here. you don’t know which f(x) the function inner most f(x) is referring to. The inner most function could either be the odd function or the even function and each one would give you a different result.
Hi WW, This is pretty tricky. You are correct that there exists potential ambiguity surrounding how f(f(x)) could be equal to 82. The clip between 1:29:40 and 1:32:00 tries to work this out. I want to allow for the possibility the the inner f(x) could be either even or odd; that's why I replace the inner f(x) with a question mark and talk through both possibilities. What we find at first is that f(x) could be 28, and then we find that it really can't be anything else. It must be 28--simply no other value will allow f(f(x)) to equal 82. Remember that the first sentence in the problem states this function only work when x is an integer, and that means that f(x) must also be an integer. In other words, all of the inputs and outputs MUST BE integers, implying that they are either odd or even. If you think you've found another possibility for f(x) that allows f(f(x)) to be equal to 82, check that all the inputs and outputs are integers. Turns out that the ambiguity that you suspected was there for f(f(x)) = 82 is ACTUALLY present once we know that f(x) = 28. There are multiple values for x itself that turns f(x) into 28.
@@jeffreyvollmer8806 Beautifully said. I reasoned that bit out after I posted the original question. I did however realize one other possible issue with the first statement. You used 82 from the question stem to plug in, however we don't have to use 82. We could try a a whole slew of values because we have the functions are defined. Would that result in a different answer?
@@saifulisfree Suppose I were given this DS question: If x = 5, Is y < 2? (1) x/y > 3 (2) y^3 - y = 0 I will plug 5 in for x in statement 1 because I know x is equal to 5. There's nothing else that it can be in this problem. I can't plug in 3 or 7 or 0, or -2 in for x, because the stem tells me "x = 5" Similarly, in that function problem, the stem tells me "f(f(x)) = 82" There's nothing else that it can be. So I would say that we do have to use 82. If I haven't managed to convince you, maybe you could give me some other values we could try? Since you mentioned that we could try a bunch of other values what do you have in mind?
because you asked so nicely: (a*b)*c =(a + b - ab)*c =a + b - ab + c - (a + b - ab)c =a + b - ab + c - (ac + bc - abc) =a + b + c - ab - ac - bc + abc a*(b*c) =a*(b + c - bc) =a + b + c - bc - a(b + c - bc) =a + b + c - bc - (ab + ac - abc) =a + b + c - bc - ab - ac + abc and that's equivalent to the previous expression, so III also is true, and the answer is (E) If I were solving this on the actual exam, I might do it this way, but I'd probably just assign values to the variables to have actual numbers at each step-I think that would be more efficient, and I'd be less likely to make a careless error involving distribution and +/- signs.
i've been trying to crack functions and this video made it so so easy. I woke up this morning not knowing how to do the function questions, and will go to bed knowing exactly how to tackle them. thank you!
I tried solving question 5 both algebraically and by picking up numbers for a, b and c and it turned out that picking up numbers is particularly quicker especially on statement 3.
One of the best teachers!
wow, you helped me so much thank you!! 5 days away from taking the test, definitely helped.
Hi, I hope you did great on your test! How would you compare the examples shown in these videos to the actual questions in the test?
How did it go? your gmat test
Wow... what a session. Learned not only the functions knowledge but also taking a calculated guess.
I do wish I could see the algebra for the symbol question, because it wasn't working out for me when I tried running through it with pen and paper. Not really that important, though, because I couldn't really take that approach on the test.
Great video I learned many things related to functions thanks
hey, in that triangle problem can we cancel x from both sides of defined equation so that we get the equation in only y form ?, it gets same -1 result.
Did you divide by x on both sides and get 1 triangle y = 2(y^2) ?
If so, essentially what you're doing is substituting '1' in for 'x'.
How did you actually do the step with -4 triangle 2 ?
I "think" you can get away with that canceling here based on how this particular function has been defined. But it's not a shortcut I'd employ on function problems universally in the future.
Hey Jeff question on the last one. I see that you assumed the nested f(x) function equals 82 because that’s what stated in the problem stem. However there is ambiguity here. you don’t know which f(x) the function inner most f(x) is referring to. The inner most function could either be the odd function or the even function and each one would give you a different result.
Hi WW, This is pretty tricky. You are correct that there exists potential ambiguity surrounding how f(f(x)) could be equal to 82. The clip between 1:29:40 and 1:32:00 tries to work this out. I want to allow for the possibility the the inner f(x) could be either even or odd; that's why I replace the inner f(x) with a question mark and talk through both possibilities.
What we find at first is that f(x) could be 28, and then we find that it really can't be anything else. It must be 28--simply no other value will allow f(f(x)) to equal 82. Remember that the first sentence in the problem states this function only work when x is an integer, and that means that f(x) must also be an integer. In other words, all of the inputs and outputs MUST BE integers, implying that they are either odd or even. If you think you've found another possibility for f(x) that allows f(f(x)) to be equal to 82, check that all the inputs and outputs are integers.
Turns out that the ambiguity that you suspected was there for f(f(x)) = 82 is ACTUALLY present once we know that f(x) = 28. There are multiple values for x itself that turns f(x) into 28.
@@jeffreyvollmer8806 Beautifully said. I reasoned that bit out after I posted the original question. I did however realize one other possible issue with the first statement. You used 82 from the question stem to plug in, however we don't have to use 82. We could try a a whole slew of values because we have the functions are defined. Would that result in a different answer?
@@saifulisfree
Suppose I were given this DS question:
If x = 5, Is y < 2?
(1) x/y > 3
(2) y^3 - y = 0
I will plug 5 in for x in statement 1 because I know x is equal to 5. There's nothing else that it can be in this problem. I can't plug in 3 or 7 or 0, or -2 in for x, because the stem tells me "x = 5"
Similarly, in that function problem, the stem tells me "f(f(x)) = 82" There's nothing else that it can be. So I would say that we do have to use 82.
If I haven't managed to convince you, maybe you could give me some other values we could try? Since you mentioned that we could try a bunch of other values what do you have in mind?
@@jeffreyvollmer8806 I see your point. Ugh lol
great
Q5 solution please....very clever teacher.....he skipped the toughest question 😂
because you asked so nicely:
(a*b)*c
=(a + b - ab)*c
=a + b - ab + c - (a + b - ab)c
=a + b - ab + c - (ac + bc - abc)
=a + b + c - ab - ac - bc + abc
a*(b*c)
=a*(b + c - bc)
=a + b + c - bc - a(b + c - bc)
=a + b + c - bc - (ab + ac - abc)
=a + b + c - bc - ab - ac + abc
and that's equivalent to the previous expression, so III also is true, and the answer is (E)
If I were solving this on the actual exam, I might do it this way, but I'd probably just assign values to the variables to have actual numbers at each step-I think that would be more efficient, and I'd be less likely to make a careless error involving distribution and +/- signs.
@@jeffreyvollmer8806 Thanks mate! Apologies for the previous comment!
@@sarthaksarode3982 Ah no worries. I probably should have included it initially anyway.
Fangirling over Jeffrey