# Question 333f1

Aug 20, 2016

There is a difference between inverse and inverse function.
See explanation for the solutions

#### Explanation:

$\textcolor{b l u e}{\text{Case 1 - Inverse}}$

$\frac{1}{h \left(x\right)} = \frac{1}{- 3 x - 3} \to - \frac{1}{3 x + 3}$

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$\textcolor{b l u e}{\text{Case 2 - Inverse function}}$

Set $h \left(x\right) = y = - 3 x - 3$

$y + 3 = - 3 x$

Multiply both sides by (-1)

$- y - 3 = + 3 x$

Divide both sides by 3

$- \frac{y}{3} - 1 = x$

Where there is $x$ write $y$ and where there is $y$ write $x$ giving:

$- \frac{x}{3} - 1 = y$

$y = - \frac{x}{3} - 1$
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The inverse function is a reflection of the original function about $y = x$