SOLVED:85-88 Domain of a Composition Find the functions f \circ g and g \circ f and their domains. f(x)=\log x, \quad g(x)=x^{2}

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Problem 88 Easy Difficulty

$85-88$ Domain of a Composition Find the functions $f \circ g$ and
$g \circ f$ and their domains.
$$f(x)=\log x, \quad g(x)=x^{2}$$

Answer

$$
\begin{array}{ll}{(f \circ g)(x)=\log \left(x^{2}\right)} & {, D_{f \circ g}=\mathbb{R} \backslash\{0\}} \\ {(g \circ f)(x)=(\log x)^{2}} & {, D_{g o f}=[0, \infty)}\end{array}
$$

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James Stewart, Lothar Redlin, Saleem Watson

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Kristen K.

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Absolute Value - Example 1

Absolute Value - Example 2

$$\begin{array}{ll}{(f \circ g)(x)=\log \left(x^{2}\right)} & {, D_{f \circ g}=\mathbb{R} \backslash\{0\}} \\ {(g \circ f)(x)=(\log x)^{2}} & {, D_{g o f}=[0, \infty)}\end{array}$$

Algebra and Trigonometry

Alayna H.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

James Stewart, Lothar Redlin, Saleem WatsonAlgebra and Trigonometry

Alayna H.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

$$
\begin{array}{ll}{(f \circ g)(x)=\log \left(x^{2}\right)} & {, D_{f \circ g}=\mathbb{R} \backslash\{0\}} \\ {(g \circ f)(x)=(\log x)^{2}} & {, D_{g o f}=[0, \infty)}\end{array}
$$

James Stewart, Lothar Redlin, Saleem Watson

Algebra and Trigonometry