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Answer 1 · 2016-08-20T22:00:36

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

$Case 1 - Inverse$ $color(blue)("Case 1 - Inverse")$

$\frac{1}{h (x)} = \frac{1}{- 3 x - 3} \to - \frac{1}{3 x + 3}$ $1/(h(x)) = 1/(-3x-3) -> -1/(3x+3)$

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$Case 2 - Inverse function$ $color(blue)("Case 2 - Inverse function")$

Set $h (x) = y = - 3 x - 3$ $h(x)=y=-3x-3$

Add 3 to both sides

$y + 3 = - 3 x$ $y+3=-3x$

Multiply both sides by (-1)

$- y - 3 = + 3 x$ $-y-3=+3x$

Divide both sides by 3#

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

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

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

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