Math Problem Statement

Let f(x) = √(x + 1), g(x) = 2x - 5, and h(x) = 3x^2 - 3. Find the indicated value f(g(4)).

Solution

To solve f(g(4))f(g(4)) based on the given functions:

  • f(x)=x+1f(x) = \sqrt{x + 1}
  • g(x)=2x5g(x) = 2x - 5

We need to:

  1. First, evaluate g(4)g(4): g(4)=2(4)5=85=3g(4) = 2(4) - 5 = 8 - 5 = 3

  2. Now, use this result to evaluate f(g(4))=f(3)f(g(4)) = f(3): f(3)=3+1=4=2f(3) = \sqrt{3 + 1} = \sqrt{4} = 2

Thus, f(g(4))=2f(g(4)) = 2.

Would you like more details or further clarification?

Here are 5 related questions for practice:

  1. What is f(g(2))f(g(2)) with the same functions?
  2. If h(x)=3x23h(x) = 3x^2 - 3, what is h(g(4))h(g(4))?
  3. Can you find the inverse of f(x)=x+1f(x) = \sqrt{x+1}?
  4. What is f(f(4))f(f(4)) for the same f(x)f(x)?
  5. How does the composition of two functions work in general?

Tip: Always solve the inner function first when evaluating a composition of functions!

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Math Problem Analysis

Mathematical Concepts

Function Composition
Square Root Functions
Linear Functions

Formulas

f(x) = √(x + 1)
g(x) = 2x - 5

Theorems

Function Composition Theorem

Suitable Grade Level

Grades 9-10