Answer:
YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
Step-by-step explanation:
Given
Given that the function f(x) and g(x) are inverse functions.
[tex]f\left(x\right)\:=\:\frac{1}{3}x\:+\:5[/tex]
[tex]g(x) = 3x - 15[/tex]
To determine
Let us determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
Determining the inverse function of f(x)
A function g is the inverse function of f if for y = f(x), x = g(y)
[tex]y=\frac{1}{3}x+5[/tex]
Replace x with y
[tex]x=\frac{1}{3}y+5[/tex]
Solve for y
[tex]y=3x-15[/tex]
Therefore,
YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
