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Use the definition of inverses to determine whether f and g are inverses.Xf(x)=2x-8, g(x) = 2 +4Are the f and g inverses of each other?OYesO №o***

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SOLUTION

For f and g to be inverses, then

[tex]f(g(x))=g(f(x))=x[/tex]

Now

[tex]\begin{gathered} f(g(x))=2(\frac{x}{2}+4)-8 \\ =\frac{2x}{2}+8-8 \\ =x \end{gathered}[/tex]

Also

[tex]\begin{gathered} g(f(x))=\frac{2x-8}{2}+4 \\ =\frac{2x-8+8}{2} \\ =\frac{2x}{2} \\ =x \end{gathered}[/tex]

Since we got x in both cases, hence f and g are inverses of each other

The answer is YES

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