Answer:
[tex]f^{-1}(x)=\dfrac{x}{\boxed{5}}+\boxed{3}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=5x-15[/tex]
An inverse function is a reflection of the function in the line y = x.
To find the inverse of the given function, replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=5x-15[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+15=5x-15+15[/tex]
[tex]\implies y+15=5x[/tex]
[tex]\implies 5x=y+15[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{y}{5}+\dfrac{15}{5}[/tex]
[tex]\implies x=\dfrac{y}{5}+3[/tex]
Replace x with f⁻¹(x) and y with x. This is the inverse function:
[tex]\implies f^{-1}(x)=\dfrac{x}{5}+3[/tex]
Learn more about inverse functions here:
https://brainly.com/question/28049700
