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For each pair of function f and g below, find f(g(x)) and g(f(x)). Then determine whether f and g are inverses of each other. Simplify your answers as much as possible. Assume your expressions are defined for all x in the domain of the composition.

1. f(x) = 1/3x, x not equal to 0



g(x) = 1/3x, x not equal to 0 what does f(g(x)) =, what does g(f(x)) =, Is f and g inverses of each other?

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tramserran

Answer:     f and g ARE INVERSES of each other

Step-by-step explanation:

If f and g are inverses of each other, then their composition will equal x.

[tex]\text{Given:}\quad f(x)=\dfrac{1}{3x}\qquad \qquad g(x)=\dfrac{1}{3x}[/tex]

[tex]f(g(x))\\\\f\bigg(\dfrac{1}{3x}\bigg)=\dfrac{1}{3(\frac{1}{3x})}\quad =\dfrac{1}{\frac{1}{x}}\quad =x\\\\\\\\\\g(f(x))\\\\g\bigg(\dfrac{1}{3x}\bigg)=\dfrac{1}{3(\frac{1}{3x})}\quad =\dfrac{1}{\frac{1}{x}}\quad =x[/tex]

Since their compositions both equal "x", they are inverses of each other

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