Math  /  Algebra

QuestionFind f(g(x))f(g(x)) and g(f(x))g(f(x)) and determine whether the pair of functions ff and gg are inverses of each other. f(x)=8x+3 and g(x)=x38f(x)=8 x+3 \text { and } g(x)=\frac{x-3}{8} a. f(g(x))=f(g(x))= \square (Simplify your answer.)

Studdy Solution
Simplify f(g(x)) f(g(x)) .
f(x38)=8(x38)+3 f\left(\frac{x-3}{8}\right) = 8\left(\frac{x-3}{8}\right) + 3
Distribute the 8: =x3+3 = x - 3 + 3
Simplify: =x = x
The simplified expression for f(g(x)) f(g(x)) is x \boxed{x} .

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