Z00078. For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other. (a) f(x) = 1/(2x), x ≠ 0 ; g(x) = 1/(2x), x ≠ 0 (b) (a) f(x) = x - 6 ; g(x) = x - 6.

Z00078. For each pair of functions 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 that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)

$\dpi{120} (a)\; f(x)=\frac{1}{2x},\; x \neq 0\;;\; \; g(x)=\frac{1}{2x},\; x\neq 0$

$\dpi{120} (b)\; f(x)=x-6\; ;\; \; g(x)=x-6$

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Z00078. For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other. (a) f(x) = 1/(2x), x ≠ 0 ; g(x) = 1/(2x), x ≠ 0 (b) (a) f(x) = x – 6 ; g(x) = x – 6.

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