se the pair of functions to find f(g(x)) and g (f (z)). Simplify your answers. f(x)=√x+6, g(x)=x² + 3 f(g(x)) =

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 82E
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**Composite Functions**

Use the pair of functions to find \(f(g(x))\) and \(g(f(x))\). Simplify your answers.

Given:
\[ f(x) = \sqrt{x + 6} \quad \text{and} \quad g(x) = x^2 + 3 \]

1. \( f(g(x)) = \)

   \[ \boxed{ } \]

2. \( g(f(x)) = \)

   \[ \boxed{ } \]
Transcribed Image Text:**Composite Functions** Use the pair of functions to find \(f(g(x))\) and \(g(f(x))\). Simplify your answers. Given: \[ f(x) = \sqrt{x + 6} \quad \text{and} \quad g(x) = x^2 + 3 \] 1. \( f(g(x)) = \) \[ \boxed{ } \] 2. \( g(f(x)) = \) \[ \boxed{ } \]
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