[SOLVED] Function Question

**looi76** · May 2nd 2008, 06:11 AM

Question:
The functions f and g are defined by:
$f : x \mapsto 3x + 2$ ███ $x \in \Re$

$g : x \mapsto \frac{6}{2x + 3}$ ███ $x \neq 1.5$

(i)...
(ii)...
(iii) Express each of $f^{-1}(x)$ and $g^{-1}(x)$ in terms of $x$ , and solve the equation $f^{-1}(x) = g^{-1}(x)$

Attempt:

$f(x) = 3x + 2$
$y = 3x + 2$
$y - 2 = 3x$
$\frac{y - 2}{3} = x$

$f^{-1}(x) = \frac{x - 2}{3}$

$g(x) = \frac{6}{2x + 3}$

I don't know how to get the inverse of g(x)

**flyingsquirrel** · May 2nd 2008, 06:21 AM

Hi

The same idea should work :

$y=\frac{6}{2x+3}$

You want an equality starting by $x=\ldots$ so multiply both sides by $2x+3$ and then bring $y$ to the right hand side.

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