Question

Let h(x)=xg(x), where g(x)=the inverse of f(x). Find h'(5) using the chart.....(type that in a minute)

Answer 1

x: 2, 3, 5
f(x): 4, 5, 1
f'(x): -1, 2, 3

Answer 2

Let's make the table for g(x)=f-1(x)
x = 4 5 1
g(x)=2 3 5

h(x)=xg(x)
h'(x)=g(x)+xg'(x) [product rule]

Apply
f'^1(x)=1/f'(f^-1(x))
g'(x)=1/(f'(g(x)))
g'(5)=1/f'(g(5))
=1/f'(3)
=1/2

Substitute in above
h'(5)=g(5)+5g'(5)
=3+5*(1/2)
=11/2