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

1 Answer
Jim G.
Apr 30, 2018

"see explanation"

Explanation:

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

"then they are inverse functions"

f(g(x))=f(1/2x+2)

color(white)(f(g(x)))=2(1/2x+2)-4

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

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

color(white)(g(f(x)))=1/2(2x-4)+2

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

rArrf(x)" and "g(x)" are inverse functions"

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