The inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]x=g(y)=-\frac{y}{3}+1[/tex].
How to find the inverse of a function of type y=f(x)=ax+b?
- An inverse function is a function that undoes the action of another function. For example, if the function [tex]f[/tex] produces the number [tex]y[/tex] after applying on [tex]x[/tex] i.e., [tex]y=f(x)[/tex], then the inverse function of [tex]f[/tex], which is denoted by [tex]f^{-1}[/tex], produces [tex]x[/tex] after applying on [tex]y[/tex] i.e., [tex]f^{-1}(y)=x[/tex].
- To find the inverse of a function of type [tex]y=f(x)=ax+b[/tex], we just need to rewrite the equation as [tex]x=g(y)[/tex] which can be illustrated as follows: [tex]y=ax+b\Longrightarrow x=\frac{y}{a}-\frac{b}{a}[/tex] i.e., [tex]g(x)=\frac{x}{a}-\frac{b}{a}[/tex] is the inverse function of [tex]f(x)=ax+b[/tex].
Here, the given function is [tex]f(x)=-3x+3[/tex].
Then we get:
[tex]y=-3x+3\\\Longrightarrow x=-\frac{y}{3}+1[/tex]
Thus, the inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]g(x)=-\frac{x}{3}+1[/tex].
The graph representing this inverse function is given as follows:
To know more about inverse function, refer: https://brainly.com/question/3831584
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