Question

given $f(x)=x + 1$ and $g(x)=x^{2}$, what is $(gcirc f)(x)$?
$(gcirc f)(x)=x^{2}+1$
$(gcirc f)(x)=x^{2}+x + 1$
$(gcirc f)(x)=(x + 1)^{2}$
$(gcirc f)(x)=x^{2}(x + 1)$

Explanation:

Step1: Define composite function

$(g \circ f)(x) = g(f(x))$

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

Substitute $f(x)=x+1$ into $g(t)=t^2$:
$g(f(x)) = (x+1)^2$

Answer:

$(g \circ f)(x) = (x + 1)^2$