Math Problem Statement

Given the functions f(x) = x - 1, g(x) = (x + 2)/5, and h(x) = 3x + 5, find F^{-1}(x) if F(x) = f(g(h(x))).

Solution

To address the questions from the image:

Problem 9

We are given:

  • f(x)=x−1f(x) = x - 1
  • g(x)=x+25g(x) = \frac{x + 2}{5}
  • h(x)=3x+5h(x) = 3x + 5

If F(x)=f(g(h(x)))F(x) = f(g(h(x))), we are asked to find F−1(x)F^{-1}(x).

Solution Steps:

  1. First, calculate h(g(f(x)))h(g(f(x))): h(x)=3x+5h(x) = 3x + 5 Substitute xx in ff, gg with h(x)h(x)

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Math Problem Analysis

Mathematical Concepts

Function Composition
Inverse Functions

Formulas

f(g(h(x)))
Inverse function formula for linear functions

Theorems

Function composition properties
Inverse function properties

Suitable Grade Level

Grades 11-12

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