For the linear function y = f ( x ) = 2 x + 9 :

Question

a. Find df/dx at x=-5

f'(-5)=_________

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

f^-1(y)=_________

c. Find df^-1/dy at y=f(-5)

(f^-1)'(f(-5))=_________

Answer 1

a) f'(x) = 2 regardless of the value of x

b) just switch x and y and solve for y

x = 2y+9, 2y=x-9, y = x/2 - 9/2

f^-1(x) = x/2 - 9/2

c) f^-1(-5) = -5/2 -9/2 = -14/2 = -7