Answer:
[tex]f^{-1}(x)=\frac{2-x}{3}[/tex]
Yes, it is a function.
Step-by-step explanation:
We have been given the function [tex]f(x)=-3x+2[/tex]
Substitute y = f(x)
[tex]y=-3x+2[/tex]
Now, interchange the position of x and y, we get
[tex]x=-3y+2[/tex]
Now, solve the equation for y
[tex]x-2=-3y[/tex]
Divide both sides by -3
[tex]\frac{x-2}{-3}=y\\\\y=\frac{2-x}{3}[/tex]
Therefore, the inverse function is
[tex]f^{-1}(x)=\frac{2-x}{3}[/tex]
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.
