Question

select the correct answer. consider these functions: f(x) = x + 1, g(x) = \frac{2}{x}. which polynomial is equivalent to (f \circ g)(x)? a. \frac{2}{x + 1} b. \frac{2x + 2}{x} c. \frac{2}{x} + 1 d. \frac{2}{x^2 + x}

Explanation:

Step1: Recall function composition

The composition \((f \circ g)(x)\) means \(f(g(x))\). So we substitute \(g(x)\) into \(f(x)\).

Step2: Substitute \(g(x)\) into \(f(x)\)

Given \(f(x) = x + 1\) and \(g(x)=\frac{2}{x}\), we replace \(x\) in \(f(x)\) with \(g(x)\). So \(f(g(x))=g(x)+1\).
Substitute \(g(x)=\frac{2}{x}\) into the above: \(f(g(x))=\frac{2}{x}+1\).

Answer:

C. \(\frac{2}{x} + 1\)