1, assuming that the slope of curve y = f (- 1) (x) at (4,7) is 4/5, find f'(y).

2. If f(x)=x? +x+ 1, find the value of (f (- 1))' (3)

Subject 1

Solution: Because y = f (- 1) (x) = g (x) is the inverse function of x=f(y), so

dx/dy = f '(y)= 1/g '(x)= 1/(4/5)= 5/4

Topic 2

Solution: according to the meaning of the question, x? +x+ 1=3, then x= 1. And because f'(x)=(x? +x+ 1)'=3x？ +1, so

(f^(- 1))'(3)= 1/f'( 1)= 1/(3× 1？ + 1)= 1/4。