Is f(x) the inverse function of g(x)? f(x) = x g(x) = –4x Choices: [[yes][no]]

Calculate (f∘g)(x): To check if f(x) is the inverse of g(x), calculate (f∘g)(x) and see if it equals x. (f∘g)(x) = f(g(x)) = f(-4x) = -4xCalculate (g∘f)(x): Now, calculate (g∘f)(x) and see if it equals x. (g∘f)(x) = g(f(x)) = g(x) = -4xCheck for Inverses: Check if (f∘g)(x) = x and (g∘f)(x) = x for f(x) and g(x) to be inverses. (f∘g)(x) = -4x != x and (g∘f)(x) = -4x != x So, f(x) is not the inverse of g(x).

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Is $f(x)$ the inverse function of $g(x)$ ? $\newline$ $f(x) = x$ $\newline$ $g(x) = -4x$ $\newline$ Choices: $\newline$ $\text{[yes]}$ $\newline$ $\text{[no]}$

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Math Problems

Algebra 2

Identify inverse functions

Full solution

Q. Is

f(x)

the inverse function of

g(x)

\newline

f(x) = x

\newline

g(x) = -4x

\newline

Choices:

\newline

\text{[yes]}

\newline

\text{[no]}

Calculate $(f\circ g)(x)$ : To check if $f(x)$ is the inverse of $g(x)$ , calculate $(f\circ g)(x)$ and see if it equals $x$ . $\newline$ $(f\circ g)(x) = f(g(x)) = f(-4x) = -4x$
Calculate $(g\circ f)(x)$ : Now, calculate $(g\circ f)(x)$ and see if it equals $x$ . $(g\circ f)(x) = g(f(x)) = g(x) = -4x$
Check for Inverses: Check if $(f\circ g)(x) = x$ and $(g\circ f)(x) = x$ for $f(x)$ and $g(x)$ to be inverses. $\newline$ $(f\circ g)(x) = -4x \neq x$ and $(g\circ f)(x) = -4x \neq x$ $\newline$ So, $f(x)$ is not the inverse of $g(x)$ .