How do you verify if $f (x) = 2 x - 4; g (x) = \frac{1}{2} x + 2$ $f(x)=2x-4; g(x)=1/2x+2$ are inverse functions?

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How do you verify if $f (x) = 2 x - 4; g (x) = \frac{1}{2} x + 2$ $f(x)=2x-4; g(x)=1/2x+2$ are inverse functions?

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Answer 1 · 2018-04-30T17:30:07

$see explanation$ $"see explanation"$

Explanation:

$if f (g (x)) = x and g (f (x)) = x$ $"if "f(g(x))=x" and "g(f(x))=x$

$then they are inverse functions$ $"then they are inverse functions"$

$f (g (x)) = f (\frac{1}{2} x + 2)$ $f(g(x))=f(1/2x+2)$

$f (g (x)) = 2 (\frac{1}{2} x + 2) - 4$ $color(white)(f(g(x)))=2(1/2x+2)-4$

$f (g (x)) = x + 4 - 4 = x$ $color(white)(f(g(x)))=x+4-4=x$

$g (f (x)) = g (2 x - 4)$ $g(f(x))=g(2x-4)$

$g (f (x)) = \frac{1}{2} (2 x - 4) + 2$ $color(white)(g(f(x)))=1/2(2x-4)+2$

$g (f (x)) = x - 2 + 2 = x$ $color(white)(g(f(x)))=x-2+2=x$

$\Rightarrow f (x) and g (x) are inverse functions$ $rArrf(x)" and "g(x)" are inverse functions"$

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How do you verify if $f (x) = 2 x - 4; g (x) = \frac{1}{2} x + 2$ $f(x)=2x-4; g(x)=1/2x+2$ are inverse functions?

1 Answer

Explanation:

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How do you verify if $f (x) = 2 x - 4; g (x) = \frac{1}{2} x + 2$ $f(x)=2x-4; g(x)=1/2x+2$ are inverse functions?