Write an expression for the inverse of
\[
f(x)=\frac{2}{3} x-5
\]
\[
f^{-1}(x)=
\]

Answer

Expert–verified

Hide Steps

Answer

\(f^{-1}(x) = \boxed{\frac{3}{2}x + \frac{15}{2}}\)

Steps

Step 1 ：Given function: \(f(x) = \frac{2}{3}x - 5\)

Step 2 ：Swap x and y: \(x = \frac{2}{3}y - 5\)

Step 3 ：Solve for y: \(y = \frac{3}{2}x + \frac{15}{2}\)

Step 4 ：\(f^{-1}(x) = \boxed{\frac{3}{2}x + \frac{15}{2}}\)