Question

find the inverse of the function f(x) = 5/6x +10

Answer 1

Answer:

$\displaystyle f^{-1}(x)=\frac{6x-60}{5}$

Step-by-step explanation:

Inverse function

Given the function

$\displaystyle f(x)=\frac{5}{6}x+10$

We find its inverse following the procedure below:

• Set y=f(x)

$\displaystyle y=\frac{5}{6}x+10$

• Multiply by 6:

$6y=5x+60$

• Operate:

$5x=6y-60$

• Solve for x:

$\displaystyle x=\frac{6y-60}{5}$

• Swap variables:

$\displaystyle y=\frac{6x-60}{5}$

• Make the new y the inverse function:

$\boxed{\displaystyle f^{-1}(x)=\frac{6x-60}{5}}$

This is the inverse function