[tex]f(g(x)) = x\\g(f(x)) = x[/tex]
Both functions are inverse of each other as their composition results in "x"
Step-by-step explanation:
Given functions are:
[tex]f(x) = 3x-2\\g(x) = \frac{x+2}{3}[/tex]
First of all, we have to find f(g(x))
[tex]f(g(x)) = 3g(x) -2\\=3(\frac{x+2}{3}) - 2\\=x+2-2\\=x[/tex]
Now g(f(x))
[tex]g(f(x)) = \frac{f(x)+2}{3}\\= \frac{3x-2+2}{3}\\=\frac{3x}{3}\\= x[/tex]
The composition of both function gives the same answer "x" which means that both functions are the inverse of each other.
Keywords: Functions, Composition
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