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Question

In Exercise given below, use f(x) and g(x) to find each composition. Identify its domain. Do not use a calculator. (a) (fg)(x)(f \circ g)(x) \quad (b) (gf)(x)(g \circ f)(x) \quad (c) (ff)(x)(f \circ f)(x)

f(x)=5,g(x)=xf(x)=5, \quad g(x)=x

Solution

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Answered 2 years ago
Answered 2 years ago
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Using the given value of f(x)f(x) and g(x)g(x), we will determine the value of the given functions.

Part (a),\textbf{Part (a),}

Knowing that:

(fg)(x)=f(g(x))(f\cdot g)(x)=f(g(x))

By definition:

(fg)(x)=f(x)=5\begin{aligned} (f\cdot g)(x)&=f(x)\\ &\boxed{=5} \end{aligned}

Function (fg)(x)=5(f\cdot g)(x)=5 is defined for all real numbers. Therefore, its domain is (,)(-\infin,\infin).

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