practice question for my sac tomorrow!!!!!

[sarahg51]

So tomorrow I am having a spesh SAC in the form of exam 1. I got to the last question of a practice exam and got stuck. The question is as follows:


Consider the function f : [-1, ∞) → R, f(x)=xe^x
Find, in simplest form, the gradient of the normal to the inverse function f^-1 at the point where x=e.

Thanks in advance to anyone who can help me!!

[BubbleWrapMan]

So the inverse function passes through (e, 1)



So

The gradient of the tangent of f at (1, e) is 2e, so the gradient of the tangent of the inverse at (e, 1) is and hence the gradient of the normal is -2e (negative reciprocal of tangent's gradient).

[sarahg51]

that makes so much sense!!
thankyou so much