How do you find (fg)(x) and (gf)(x) and determine if the given functions are inverses of each other $f (x) = x^{2} - 3$ $f(x) = x^2 − 3$ and $g (x) = \sqrt{x} + 3$ $g(x) = sqrtx+3$ ?

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How do you find (fg)(x) and (gf)(x) and determine if the given functions are inverses of each other $f (x) = x^{2} - 3$ $f(x) = x^2 − 3$ and $g (x) = \sqrt{x} + 3$ $g(x) = sqrtx+3$ ?

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Answer 1 · 2017-01-24T20:29:05

To find $f (g (x)) and g (f (x))$ $f(g(x)) and g(f(x))$ , substitute, g(x) for x in f(x), and f(x) for x in g(x), respectively. If they are inverses, both substitutions will equal x.

Explanation:

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

$f (g (x)) = x + 6 \sqrt{x} + 9 - 3$ $f(g(x)) = x + 6sqrt(x) + 9 -3$

$f (g (x)) = x + 6 \sqrt{x} + 6$ $f(g(x)) = x + 6sqrt(x) + 6$

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

They are not inverses, because both cases must reduce to x.

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How do you find (fg)(x) and (gf)(x) and determine if the given functions are inverses of each other $f (x) = x^{2} - 3$ $f(x) = x^2 − 3$ and $g (x) = \sqrt{x} + 3$ $g(x) = sqrtx+3$ ?

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How do you find (f*g)(x) and (g*f)(x) and determine if the given functions are inverses of each other f(x) = x^2 − 3f(x)=x2−3f(x) = x^2 − 3 and g(x) = sqrtx+3g(x)=√x+3g(x) = sqrtx+3?

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How do you find (fg)(x) and (gf)(x) and determine if the given functions are inverses of each other $f (x) = x^{2} - 3$ $f(x) = x^2 − 3$ and $g (x) = \sqrt{x} + 3$ $g(x) = sqrtx+3$ ?