Question

Let f(x)=3x-6. Is f one-to-one? If it is find f^-1, if not explain why.

Answer 1

Answer:  Yes,  $\bold{f^{-1}(x)=\dfrac{x+6}{3}}$

Step-by-step explanation:

f(x) = 3x - 6    is a line so it is a function  because

                      it passes the vertical line test

                              and the horizontal line test

To find the inverse, swap the x's and y's and solve for y

$y=3x-6\\\\\\\text{Swap the x's and y's:}\qquad x=3y-6\\\\\text{Add 6 to both sides:}\qquad x+6=3y\\\\\text{Divide both sides by 3:}\qquad \dfrac{x+6}{3}=y$