How do you prove that f(x) and g(x) are inverses of each other?

Question

$f (x) = \frac{x + 3}{2}$ $f(x)=(x+3)/2$

$g (x) = 2 x - 3$ $g(x)=2x-3$

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Answer 1 · 2016-12-20T02:49:04

If functions $f (x)$ $f(x)$ and $g (x)$ $g(x)$ are inverses, their compositions will equal $x$ $x$ .

Composition 1: $f (g (x))$ $f(g(x))$

$f (g (x)) = \frac{(2 x - 3) + 3}{2} = \frac{2 x}{2} = x \sqrt$ $f(g(x)) = ((2x - 3) + 3)/2 = (2x)/2 = x" "color(green)(√)$

Composition 2: $g (f (x))$ $g(f(x))$

$g (f (x)) = 2 (\frac{x + 3}{2}) - 3 = x + 3 - 3 = x \sqrt$ $g(f(x)) = 2((x + 3)/2) - 3 = x + 3 - 3 = x" "color(green)(√)$

Hopefully this helps!