If g is an increasing function such that g(2)=8 and g(2)=5, calculate (g1)(8).

Problem 44E

If g is an increasing function such that g(2)=8 and g(2)=5, calculate (g1)(8).

Calculus, James Stewart 8th edition
6 Inverse Functions
1. Inverse Functions
Problem no. 44E from

Step-by-Step Solution

To determine

To find: g-1'8

Answer

Answer: g-1'8=15

Explanation

Given: g2=8 and g'2=5.

Since g is an increasing function, it is one to one. Therefore, g2=8 ⇒ g-18=2.

Conclusion: By Theorem 7, g-1'8=1g'g-18=1g'2=15.