For the linear function y = f ( x ) = 2 x + 6:

Question

a). find df/dx at x=-3

I got the answer which is -2 but the next two parts I do not know how to do.

f'(x)= 2--> f'(-3)=2

b). find a formula for x=f^-1(y)

f^-1(y)=???

c). find df^-1/dy at y=f(-3)

(f^-1)'(f(-3))=???

Answer 1

OK...your first answer is correct.

To get the inverse, interchange roles of x and y and solve for y:

x=2y+6 => y=(x-6)/2...this is the inverse.

To solve the last; use implicit differentiation:

1=(1/2) (dx/dy), i.e. not surprisingly df^-1/dy = 2.

Remember what is being asked for in the last part is the derivative of the ORIGINAL function.