How do you find the inverse of $f (x) = \frac{x}{x + 3}$ $f(x)=x/(x+3)$ ?

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How do you find the inverse of $f (x) = \frac{x}{x + 3}$ $f(x)=x/(x+3)$ ?

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Answer 1 · 2015-10-27T10:12:10

Note that if $g (x)$ $g(x)$ is the inverse of $f (x)$ $f(x)$
then $f (g (x)) = x$ $f(g(x)) = x$
Solve $f (g (x)) = \frac{g (x)}{g (x) + 3} = x$ $f(g(x)) = g(x)/(g(x)+3) = x$ for $g (x)$ $g(x)$

Explanation:

Substituting $g (x)$ $g(x)$ for $x$ $x$ in the original definition of $f (x)$ $f(x)$

$f (g (x)) = \frac{g (x)}{g (x) + 3} = x$ $f(g(x)) = g(x)/(g(x)+3) = x$

$g (x) = x \cdot g (x) + x \cdot 3$ $g(x) = x*g(x) + x*3$

$g (x) - g (x) \cdot x = 3 x$ $g(x)-g(x)*x = 3x$

$g (x) (1 - x) = 3 x$ $g(x)(1-x) = 3x$

$g (x) = \frac{3 x}{1 - x}$ $g(x) = (3x)/(1-x)$

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How do you find the inverse of $f (x) = \frac{x}{x + 3}$ $f(x)=x/(x+3)$ ?

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