Find fog and go f. f(x) = ³√√√x-2, g(x) = x³ + 1 (a) fog (b) gof Find the domain of each function and each composite function. (Enter your answers using interval notation.) domain of f domain of g domain of fog domain of g of

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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## Composite Functions and Domain Determination

### Problem Statement

Find \(f \circ g\) and \(g \circ f\).

Given:

\[ f(x) = \sqrt[3]{x - 2}, \quad g(x) = x^3 + 1 \]

### Solve for Composite Functions

(a) Find \( f \circ g \)

\[ f \circ g = \square \]

(b) Find \( g \circ f \)

\[ g \circ f = \square \]

### Determine Domains

Find the domain of each function and each composite function. (Enter your answers using interval notation.)

- Domain of \( f \)

\[ \square \]

- Domain of \( g \)

\[ \square \]

- Domain of \( f \circ g \)

\[ \square \]

- Domain of \( g \circ f \)

\[ \square \]
Transcribed Image Text:## Composite Functions and Domain Determination ### Problem Statement Find \(f \circ g\) and \(g \circ f\). Given: \[ f(x) = \sqrt[3]{x - 2}, \quad g(x) = x^3 + 1 \] ### Solve for Composite Functions (a) Find \( f \circ g \) \[ f \circ g = \square \] (b) Find \( g \circ f \) \[ g \circ f = \square \] ### Determine Domains Find the domain of each function and each composite function. (Enter your answers using interval notation.) - Domain of \( f \) \[ \square \] - Domain of \( g \) \[ \square \] - Domain of \( f \circ g \) \[ \square \] - Domain of \( g \circ f \) \[ \square \]
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