Question

Given the following functions, use function composition to determine if $f(x)$ and $g(x)$ are inverse functions. $f(x) = x^2 + 3, x \ge 0$ and $g(x) = \sqrt{x - 3}$ (a) $(f \circ g)(x) = $ (b) $(g \circ f)(x) = $ (c) Thus $g(x)$ Select an answer an inverse function of $f(x)$

Name: given the following functions use function composition to determine if fx and gx are inverse functions fx x2 3 x ge 0 and gx sqrtx 3 a f circ gx b g circ fx c thus gx select an answer an inv 49336
Uploaded: 2020-06-24T06:16:42-08:00
Duration: 1 min 3 s
Channel: Ankit Gupta
Description: given the following functions use function composition to determine if fx and gx are inverse functions fx x2 3 x ge 0 and gx sqrtx 3 a f circ gx b g circ fx c thus gx select an answer an inv 49336

          Given the following functions, use function composition to determine if $f(x)$ and $g(x)$ are inverse functions.
$f(x) = x^2 + 3, x \ge 0$ and $g(x) = \sqrt{x - 3}$
(a) $(f \circ g)(x) = $
(b) $(g \circ f)(x) = $
(c) Thus $g(x)$ Select an answer an inverse function of $f(x)$

given the following functions use function composition to determine if fx and gx are inverse functions fx x2 3 x ge 0 and gx sqrtx 3 a f circ gx b g circ fx c thus gx select an answer an inv 49336

Added by Jasmine W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Ankit Gupta

06/24/2020

Step 1

$(f \circ g)(x) = f(g(x)) = f(\sqrt{x - 3}) = (\sqrt{x - 3})^2 + 3 = x - 3 + 3 = x$ Show more…

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Given the following functions, use function composition to determine if $f(x)$ and $g(x)$ are inverse functions. $f(x) = x^2 + 3, x \ge 0$ and $g(x) = \sqrt{x - 3}$ (a) $(f \circ g)(x) = $ (b) $(g \circ f)(x) = $ (c) Thus $g(x)$ Select an answer an inverse function of $f(x)$