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
[tex]\frac{8y}{8}=\frac{x-1}{8}[/tex] Divide both sides by 8 and simplify
[tex]y=\frac{x-1}{8}[/tex] Inverse equation
[tex]y=\frac{1}{8}x-\frac{1}{8}[/tex] Slope-intercept form
Use function notation, change "y"
[tex]f^{-1}(x)=\frac{x-1}{8}[/tex] Simplified
[tex]f^{-1}(x)=\frac{1}{8}x-\frac{1}{8}[/tex] Slope-intercept form
