Question

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

Answer 1

f⁻¹(x) = (x - 1)/8

Or

f⁻¹(x) = 1/8 x - 1/8

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

`(8y)/(8)=(x-1)/(8)` Divide both sides by 8 and simplify

`y=(x-1)/(8)` Inverse equation

`y=(1)/(8)x-(1)/(8)` Slope-intercept form

Use function notation, change "y"

`f^(-1)(x)=(x-1)/(8)` Simplified

`f^(-1)(x)=(1)/(8)x-(1)/(8)` Slope-intercept form