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