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

Answer:

$f^{-1}(x)=\frac{2-x}{3}$

Yes, it is a function.

Step-by-step 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

$\frac{x-2}{-3}=y\\\\y=\frac{2-x}{3}$

Therefore, the inverse function is

$f^{-1}(x)=\frac{2-x}{3}$

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.