Question

What is the inverse of the function f(x) = 8x+1

Answer 1

Answer:

f⁻¹(x) = (x - 1)/8

Or

f⁻¹(x) = 1/8 x - 1/8

Step-by-step explanation:

To find the inverse of a function, switch the "x" and "y" variables, then isolate "y".

Remember "f(x)" is the same thing as "y". Change from function notation to "y".

f(x) = 8x + 1

y = 8x + 1        

Switch the "x" and "y" variables

x = 8y + 1

Isolate "y". Move the "y" variable to the left for standard formatting

8y + 1 = x            

8y + 1 - 1 = x - 1               Subtract 1 from both sides

8y = x - 1

$\frac{8y}{8}=\frac{x-1}{8}$        Divide both sides by 8 and simplify

$y=\frac{x-1}{8}$                  Inverse equation

$y=\frac{1}{8}x-\frac{1}{8}$             Slope-intercept form

Use function notation, change "y"

$f^{-1}(x)=\frac{x-1}{8}$                      Simplified

$f^{-1}(x)=\frac{1}{8}x-\frac{1}{8}$                   Slope-intercept form