How do you find the compositions given $f (x) = \frac{x}{x + 1}$ $f(x) = x/(x + 1)$ , $g (x) = x^{2} - 1$ $g(x) = x^2 - 1$ ?

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Answer 1 · 2016-01-25T09:53:03

For f(x) the domain is $R - {1}$ $R-{1}$ and for g(x) is $R$ $R$ where $R$ $R$ is the set of real numbers.
Hence

$f (g (x)) = \frac{x^{2} - 1}{x^{2} - 1 + 1} = \frac{x^{2} - 1}{x^{2}} = 1 - \frac{1}{x^{2}}$ $f(g(x))=(x^2-1)/(x^2-1+1)=(x^2-1)/(x^2)=1-1/(x^2)$

and

$g (f (x)) = {(\frac{x}{x + 1})}^{2} - 1$ $g(f(x))=(x/(x+1))^2-1$

How do you find the compositions given f(x) = x/(x + 1)f(x)=xx+1f(x) = x/(x + 1), g(x) = x^2 - 1g(x)=x2−1g(x) = x^2 - 1?