Question

determine whether the following sentence is true or false.
$f \circ g$ is the same function as $g \circ f$.

choose the correct answer below.
\\(\bigcirc\\) true
\\(\bigcirc\\) false

Explanation:

Step1: Recall function composition

Function composition \( f \circ g \) means \( f(g(x)) \), and \( g \circ f \) means \( g(f(x)) \).

Step2: Provide a counterexample

Let \( f(x) = x + 1 \) and \( g(x) = 2x \). Then \( f \circ g(x)=f(g(x)) = 2x + 1 \), and \( g \circ f(x)=g(f(x)) = 2(x + 1)=2x + 2 \). These two functions are not the same, so \( f \circ g \) is not generally the same as \( g \circ f \).

Answer:

False