Answered

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4. Determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
Write yes or no and explain your reasoning by showing work.

Sagot :

absor201

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.

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