The function f(x)=6x+2 is​ one-to-one. Find an equation for f^-1(x) ​, the inverse function.

Answer 1

f(x)=y=6x+2

The trick to find the inverse function is to swap x and y and solve for y.

x=6y+2

6y=x-2

y=(x-2)/6 = f^-1(x) = g(x)

To check if this is he inverse function, f(g(x)) must equal x

f(g(x)) = 6((x-2)/6)+2

= x-2+2 = x

Answer 2

f(x) = 6x + 2

y= 6x + 2

switch x with y and y with x

x= 6y +2

-2=-2

x - 2 = 6y

(x- 2)/6 = y

f(x) = (X - 2)/6