Math  /  Algebra

QuestionGiven the function h(x)=(x+2)2 h(x) = (x + 2)^2 , find functions f(x) f(x) and g(x) g(x) such that h(x)=f(g(x)) h(x) = f(g(x)) .

Studdy Solution
Verify that the composition f(g(x)) f(g(x)) correctly reproduces h(x) h(x) .
Calculate f(g(x)) f(g(x)) : f(g(x))=f(x+2)=(x+2)2 f(g(x)) = f(x + 2) = (x + 2)^2
Since this matches h(x) h(x) , the functions f(x)=x2 f(x) = x^2 and g(x)=x+2 g(x) = x + 2 are correct.
Solution: The functions are f(x)=x2 f(x) = x^2 and g(x)=x+2 g(x) = x + 2 .

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