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\\) false
\\(\bigcirc\\) true

Explanation:

The composition of functions \( f \circ g \) means \( f(g(x)) \), and \( g \circ f \) means \( g(f(x)) \). These are not the same in general. For example, if \( f(x) = x + 1 \) and \( g(x) = 2x \), then \( f \circ g(x)=f(2x)=2x + 1 \) and \( g \circ f(x)=g(x + 1)=2(x + 1)=2x+2 \), which are different. So \( f \circ g \) is not the same as \( g \circ f \) in general.

Answer:

A. False