Question

question 3 1 pts combining two functions by applying the second function to the result of the first function is called the composition of functions. the notation f(g(x)) means that you can substitute g(x) for x in f(x). which of the following statements are true for f(x)=x + 1 and g(x)=2x? select all that apply. f(g(x))=2x + 1 g(f(x))=2x + 2 f(g(x))=2x + 1 g(f(x))=2(x + 1)

Explanation:

Step1: Find $f(g(x))$

Substitute $g(x)=2x$ into $f(x)$. Since $f(x)=x + 1$, then $f(g(x))=2x+1$.

Step2: Find $g(f(x))$

Substitute $f(x)=x + 1$ into $g(x)$. Since $g(x)=2x$, then $g(f(x))=2(x + 1)=2x+2$.

Answer:

$f(g(x)) = 2x + 1$ is true.
$g(f(x)) = 2x + 2$ is true.
$g(f(x)) = 2(x + 1)$ is true.