Answer:
B. \(h^{-1}(x)=\frac{-5x}{3}+\frac{5}{6}\)
Step-by-step explanation:
We have been given a function \(h(x)=-\frac{3}{5}x+\frac{1}{2}\). We are asked to find the inverse function of our given function.
First of all, we replace h(x) by y as:
\(y=-\frac{3}{5}x+\frac{1}{2}\)
To find inverse of our given function we will interchange x and y variables and solve for y.
\(x=-\frac{3}{5}y+\frac{1}{2}\)
Upon subtracting 1/2 from both sides of equation, we will get:
\(x-\frac{1}{2}=-\frac{3}{5}y+\frac{1}{2}-\frac{1}{2}\)
\(x-\frac{1}{2}=-\frac{3}{5}y\)
Let us have a common denominator.
\(\frac{2x}{2}-\frac{1}{2}=-\frac{3}{5}y\)
\(\frac{2x-1}{2}=-\frac{3}{5}y\)
Multiplying both sides by \(-\frac{5}{3}\),
\(-\frac{5}{3}*\frac{2x-1}{2}=-\frac{5}{3}*-\frac{3}{5}y\)
\(\frac{-10x+5}{2*3}=y\)
\(\frac{-10x}{6}+\frac{5}{6}=y\)
\(\frac{-5x}{3}+\frac{5}{6}=y\)
Replacing y by \(h^{-1}(x)\) we will get,
\(h^{-1}(x)=\frac{-5x}{3}+\frac{5}{6}\)
Therefore, the option B is the correct choice.
Therefore,
