At 12:09, when you restrict the domain to x is greater then or equal to 3, that still does not make the inverse a function because you would still have both arms of the parabola visible, and if you do x is less then or equal to 3 for the inverse, then you just don't see the inverse. So shouldn't we restrict the range in order to separate the sideways parabola into 2 branches?
When you restrict the domain of the original function at the vertex then you are only dealing with half of the parabola, so when you do the inverse you are only dealing with either the upper or lower branch of the parabola.
@@mshavrotscanadianuniversit6234 Oh my bad, I thought we had to restrict the domain of the inverse relation to make it a function, thanks for the clarification.
Check out the comment from baigsaba below. That might help. I’m on vacation right now. Let me know if you still need help. Also check this pdf. mrkennedy.pbworks.com/w/file/fetch/73304405/3U%20Ch.%201%20Text%20Solutions.pdf
For this question you are given an equation for the temperature in terms of the depth and you are trying to find the depth in terms of the temperature. All you are required to do is to isolate d to find the T at a given depth. You cannot switch the variables by making the depth the temperature and the temperature the depth.
Thank you for answering my previous questions Ms. Havrot. I was also wondering if we were given a quadratic such as -2(x-4)^2+5, and we had to restrict the domain of this function so its inverse is a function, it would be x is greater or equal to 4, or x is less than or equal to 4. My question how do we know which of these domains correspond to which branch (the upper or the lower)?
Best to check a few points on the function, but generally if concave down going to the right (i.e x> than your x coordinate of the vertex (4,5) [the point (5, 3) becomes (3, 5) and, checking a point to the left, the point (1, 3) becomes (3, 1) ]) then that is the top branch of the inverse
At 12:09, when you restrict the domain to x is greater then or equal to 3, that still does not make the inverse a function because you would still have both arms of the parabola visible, and if you do x is less then or equal to 3 for the inverse, then you just don't see the inverse. So shouldn't we restrict the range in order to separate the sideways parabola into 2 branches?
When you restrict the domain of the original function at the vertex then you are only dealing with half of the parabola, so when you do the inverse you are only dealing with either the upper or lower branch of the parabola.
@@mshavrotscanadianuniversit6234 Oh my bad, I thought we had to restrict the domain of the inverse relation to make it a function, thanks for the clarification.
At 4:29 you didn’t switch T and d to find inverse.
Can you please do question 7 from the textbook, I don’t really understand why we don’t switch the x and y values for some questions. Thank you.
Check out the comment from baigsaba below. That might help. I’m on vacation right now. Let me know if you still need help. Also check this pdf. mrkennedy.pbworks.com/w/file/fetch/73304405/3U%20Ch.%201%20Text%20Solutions.pdf
To find inverse we have to switch x and y. But you didn’t switch in temperature and depth question. Plz check
For this question you are given an equation for the temperature in terms of the depth and you are trying to find the depth in terms
of the temperature. All you are required to do is to isolate d to find the T at a given depth. You cannot switch the variables by making the depth the temperature and the temperature the depth.
Did u mean rearranging the variables will give you inverse function? @@mshavrotscanadianuniversit6234
I think, as worded, the question excludes d=0, as 0 is not below the surface. Does that change much?
D=0 will give you the air temperature at the surface.
Thank you for answering my previous questions Ms. Havrot. I was also wondering if we were given a quadratic such as -2(x-4)^2+5, and we had to restrict the domain of this function so its inverse is a function, it would be x is greater or equal to 4, or x is less than or equal to 4. My question how do we know which of these domains correspond to which branch (the upper or the lower)?
Best to check a few points on the function, but generally if concave down going to the right (i.e x> than your x coordinate of the vertex (4,5) [the point (5, 3) becomes (3, 5) and, checking a point to the left, the point (1, 3) becomes (3, 1) ]) then that is the top branch of the inverse
Naushad Harji Please do as many questions you can solve from the Nelson textbook. Thank you kindly.
Pick three and I’ll do them for you. I don’t have internet in my house right now. (Just data on my phone) so I’ll do them as soon as I can.