Question

(Simplify your answer.)Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. x-8 f(x) = 4x + 8 and g(x) = 4

Answer 1

• x, x, yes

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Given

• f(x) = 4x + 8,
• g(x) = (x - 8)/4.

To find

• f(g(x)),
• g(f(x)),
• Determine if f and g are inverse functions.

Solution

• f(g(x)) = 4(x - 8)/4 + 8 = x - 8 + 8 = x
• g(f(x)) = (4x - 8 + 8)/4 = 4x/4 = x
• Since both composite functions result in same value of x, they are inverses of each other.