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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:

\(1+y=10-10y\)

Adding 10y to both sides:

\(11y+1=10\)

Subtracting 1 from both sides:

\(11y=9\)

Dividing both sides by 11 gives the final answer of:

\(y=\frac{9}{11}\)

 Jan 5, 2022

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