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)=(x+6)/(3)}`

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 (x+6)/(3)=y`