Answer to Question #157218 in Calculus for Lexi

Question #157218

Express the following function, F(x), as a composition of two functions, f and g. f(g(x)).

F(x)= x^2/(x^2+4)


Verify that f(g(x)) = F(x)


1
Expert's answer
2021-01-21T20:10:37-0500

Consider "F(x)=(f \\circ g)(x)"

Composition of function is the function of a function

Therefore, "F(x)=f(g(x))"

"F(x)=\\frac{x^2}{x^2+4}"

F(x) is a function of f(x) and therefore "f(x)=\\frac{x}{x+4}" and F(x) is power 2 of x.

Hence g(x)=x2

In conclusion, "f(x)=\\frac{x}{x+4}" and g(x)=x2

F(x)=f(g(x)) ="\\frac{x^2}{x^2+4}"



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