If h(y) = (1 + y)/(2 - 2y), then what is the value of $h^{-1}(5)$? Express your answer in simplest form.
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:
\(y=\frac{9}{11}\)