What is the inverse function of $g (x) = 3 \sqrt{x - 8}$ $g(x)=3sqrt(x-8)$ ?

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What is the inverse function of $g (x) = 3 \sqrt{x - 8}$ $g(x)=3sqrt(x-8)$ ?

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Answer 1 · 2015-10-27T10:21:23

If $h (x)$ $h(x)$ is the inverse of $g (x)$ $g(x)$
then $h (x) = \frac{x^{2} + 72}{9}$ $h(x) = (x^2+72)/9$

Explanation:

Note that if $h (x)$ $h(x)$ is the inverse of $g (x)$ $g(x)$
$XXX g (h (x)) = x$ $color(white)("XXX")g(h(x))=x$
and
substituting $h (x)$ $h(x)$ for $x$ $x$ in the original definition of $g (x)$ $g(x)$
$XXX g (h (x)) = 3 \sqrt{h (x) - 8}$ $color(white)("XXX")g(h(x)) = 3sqrt(h(x)-8)$

Therefore
$XXX 3 \sqrt{h (x) - 8} = x$ $color(white)("XXX")3sqrt(h(x)-8)=x$

$XXX \sqrt{h (x) - 8} = \frac{x}{3}$ $color(white)("XXX")sqrt(h(x)-8) = x/3$

$XXX h (x) - 8 = \frac{x^{2}}{9}$ $color(white)("XXX")h(x)-8 = x^2/9$

$XXX h (x) = \frac{x^{2} + 72}{9}$ $color(white)("XXX")h(x) = (x^2+72)/9$

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What is the inverse function of $g (x) = 3 \sqrt{x - 8}$ $g(x)=3sqrt(x-8)$ ?

1 Answer

Explanation:

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What is the inverse function of g(x)=3√x−8g(x)=3sqrt(x-8)?

1 Answer

Explanation:

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What is the inverse function of $g (x) = 3 \sqrt{x - 8}$ $g(x)=3sqrt(x-8)$ ?