How do you find the compositions given $f (x) = ∣ x - 2$ $f(x) = |x - 2$ |, $g (x) = \sqrt{x}$ $g(x) = sqrtx$ ?

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How do you find the compositions given $f (x) = ∣ x - 2$ $f(x) = |x - 2$ |, $g (x) = \sqrt{x}$ $g(x) = sqrtx$ ?

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Answer 1 · 2018-07-05T08:58:50

$f (g (x)) = f (\sqrt{x}) = ∣ ∣ \sqrt{x} - 2 ∣ ∣$ $f(g(x))=f(sqrt(x))=|sqrt(x)-2|$ and $g (f (x)) = g (| x - 2 |) = \sqrt{| x - 2 |}$ $g(f(x))=g(|x-2|)=sqrt(|x-2|)$

Explanation:

Every function has an input and an output. Composing two functions means to use the output of the first as the input for the second.

So, $f (x)$ $f(x)$ takes an input $x$ $x$ and outputs the absolute value of the input minus two.
$g (x)$ $g(x)$ takes an input $x$ $x$ and ouputs the square root of the input.

So, $f (g (x)) = f (\sqrt{x}) = ∣ ∣ \sqrt{x} - 2 ∣ ∣$ $f(g(x))=f(sqrt(x))=|sqrt(x)-2|$ and $g (f (x)) = g (| x - 2 |) = \sqrt{| x - 2 |}$ $g(f(x))=g(|x-2|)=sqrt(|x-2|)$

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How do you find the compositions given $f (x) = ∣ x - 2$ $f(x) = |x - 2$ |, $g (x) = \sqrt{x}$ $g(x) = sqrtx$ ?

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Explanation:

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How do you find the compositions given f(x) = |x - 2f(x)=∣x−2f(x) = |x - 2|, g(x) = sqrtxg(x)=√xg(x) = sqrtx?

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Explanation:

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How do you find the compositions given $f (x) = ∣ x - 2$ $f(x) = |x - 2$ |, $g (x) = \sqrt{x}$ $g(x) = sqrtx$ ?