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Base on definition of the inverse, f(g(x))=x and vice versa. Given f(x)=1/2x+3 and g(x)=2x-6, write a composition (s) should be used to prove that f(x) and g(x) are inverses of each other.

Base on definition of the inverse fgxx and vice versa Given fx12x3 and gx2x6 write a composition s should be used to prove that fx and gx are inverses of each o class=


Answer :

To verifiy if these are inverses we need to calculate the expression "f(g(x))" which uses the expression for "g(x)" in place of x on the expression of "f(x)". We have:

[tex]\begin{gathered} f(g(x))=\frac{1}{2}(2x-6)+3 \\ f(g(x))=\frac{2x}{2}-\frac{6}{2}+3 \\ f(g(x))=x-3+3 \\ f(g(x))=x \end{gathered}[/tex]

Since the result is f(g(x)) = x, they are inverses of each other.

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