Math  /  Algebra

QuestionFor each pair of functions ff and gg below, find f(g(x))f(g(x)) and g(f(x))g(f(x)). Then, determine whether ff and gg are inverses of each other.
Simplify your answers as much as possible. (Assume that your expressions are defined for all xx in the domain of the composition. You do not have to indicate the domain.) (a) f(x)=2x,x0f(x)=\frac{2}{x}, x \neq 0 (b) f(x)=3x7f(x)=3 x-7 g(x)=2x,x0f(g(x))=xg(f(x))=x\begin{array}{l} g(x)=\frac{2}{x}, x \neq 0 \\ f(g(x))=x \\ g(f(x))=x \end{array} ff and gg are inverses of each other ff and gg are inverses of each other ff and gg are not inverses of each other ff and gg are not inverses of each other

Studdy Solution
For the first pair, f(g(x))=xf(g(x)) = x and g(f(x))=xg(f(x)) = x, so they *are* inverses.
For the second pair, f(g(x))=6x7f(g(x)) = \frac{6}{x} - 7 and g(f(x))=23x7g(f(x)) = \frac{2}{3x - 7}, so they are *not* inverses.

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