Question

Let f be the function defined by f(x)= 5cos(pix) - e^(x^2 -4). If g(x)= inverse of f(x), find the equation of the line tangent to the graph if g at point where g(x)=2

I would just like to check that I understood how to do this properly...
derivative of f(x) = -5pisin(pix) -2xe^(x^2 -4)
Plug in 2 for x -> -4
slopes of inverse functions are reciprocals so slope at g(x)=2 would be -1/4
Then plugging in 2 for x into f(x) because g(x)=2 means f(2)=x
So gets point (4,2) in terms of g

So I get y= -1/4 (x-4) +2 as the tangent line? :3

Answer 1

The app doesn't have a bump button ;-;

Answer 2

@mathmale could you check if you're not too busy? :3