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# Inverse Functions

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If h(y) = (1 + y)/(2 - 2y), then what is the value of $h^{-1}(5)$? Express your answer in simplest form.

Jan 5, 2022

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Answer: $$\frac{9}{11}$$

Explanation:

What this is basically asking is for what value of y does $$\frac{1+y}{2-2y}$$ equal to 5.

Multiplying both sides by 2-2y:

$$1+y=5(2-2y)$$

Distribution:

$$1+y=10-10y$$

$$11y+1=10$$

Subtracting 1 from both sides:

$$11y=9$$

Dividing both sides by 11 gives the final answer of:

$$y=\frac{9}{11}$$

Jan 5, 2022