Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{3}x+5}[/tex]
Step-by-step explanation:
[tex]f(x)=3x-15\to y=3x-15\\\\\text{exchange x to y and vice versa:}\ x=3y-15\\\\\text{solve for}\ y:\\\\3y-15=x\qquad\text{add 15 to both sides}\\\\3y=x+15\qquad\text{divide both sides by 3}\\\\y=\dfrac{x}{3}+5\\\\y=\dfrac{1}{3}x+5[/tex]
