Question

f(x) = √x and g(x) = 2x² + 3 find g(f(x)).

Explanation:

Step1: Understand function composition

To find \( g(f(x)) \), we substitute \( f(x) \) into \( g(x) \). That is, wherever there is an \( x \) in \( g(x) \), we replace it with \( f(x) \).

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

Given \( f(x)=\sqrt{x} \) and \( g(x) = 2x^{2}+3 \). Substitute \( \sqrt{x} \) for \( x \) in \( g(x) \):
\( g(f(x))=g(\sqrt{x})=2(\sqrt{x})^{2}+3 \)

Step3: Simplify the expression

We know that \( (\sqrt{x})^{2}=x \) (for \( x\geq0 \) since we have a square root in \( f(x) \)). So,
\( 2(\sqrt{x})^{2}+3 = 2x + 3 \)

Answer:

\( g(f(x)) = 2x + 3 \) (for \( x\geq0 \))