Question

Find the inverse of f(x)=−3/2x+7/2.

Answer 1

Answer: $f^{-1}(x)=-\frac{2}{3}x+\frac{7}{3}$

Step-by-step explanation:

To find the inverse of a function, you want to replace x with y and y with x. Then, you solve for y.

$y=-\frac{3}{2}x+\frac{7}{2}$                       [replace y with x and x with y]

$x=-\frac{3}{2}y+\frac{7}{2}$                       [subtract both sides by 7/2]

$x-\frac{7}{2} =-\frac{3}{2}y$                       [multiply both sides by -2/3]

$-\frac{2}{3} (x-\frac{7}{2} )=y$                     [distribute]

$y=-\frac{2}{3}x+\frac{7}{3}$

Now, we have our inverse function.

$f^-^1(x)=-\frac{2}{3}x+\frac{7}{3}$