Given $f (x) = 4 - x^{2}$ $f(x)=4-x^2$ and $g (x) = | 2 x - 7 |$ $g(x)=|2x-7|$ , how do you find f(g(2)) and g(f(2))?

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Answer 1 · 2017-02-14T02:47:13

$f (g (2)) = - 5 and g (f (2)) = 7$ $f(g(2))=-5 and g(f(2))=7$ .

$f (g (2)) = 4 - {(g (2))}^{2} = 4 - {(| 4 - 7 |)}^{2} = 4 - 9 = - 5$ $f(g(2))=4-(g(2))^2=4-(|4-7|)^2=4-9=-5$ .

$g (f (2)) = ∣ ∣ 2 (4 - 2^{2}) - 7 ∣ ∣ = | - 7 | = 7$ $g(f(2))=|2(4-2^2)-7|=|-7|=7$ .

Given f(x)=4−x2f(x)=4-x^2 and g(x)=|2x−7|g(x)=|2x-7|, how do you find f(g(2)) and g(f(2))?