Question

Find f^-1(x) for f(x)=-3x+2 and state whether or not it is a function.

Answer 1

x = -3y + 2

-3y = x - 2

f^-1(x) = y = -(x-2)/3

The inverse here is just a straight line so it is a function.

Answer 2

`f^(-1)(x)=(2-x)/(3)`

Yes, it is a function.

Explanation:

We have been given the function
`f(x)=-3x+2`

Substitute y = f(x)

`y=-3x+2`

Now, interchange the position of x and y, we get

`x=-3y+2`

Now, solve the equation for y

`x-2=-3y`

Divide both sides by -3

`(x-2)/(-3)=y\\\\y=(2-x)/(3)`

Therefore, the inverse function is

`f^(-1)(x)=(2-x)/(3)`

The given function, it represents a linear equation and the graph is a straight line which is not vertical. Hence, we can say that it must pass the vertical line test.

In other words, for every x, we have a unique y.

Hence, it is a function.