Let f : R → R, g : R → R be two functions defined by

Question:

Let $f: R \rightarrow R, g: R \rightarrow R$ be two functions defined by $f(x)=x^{2}+x+1$ and $g(x)=1-x^{2}$. Write fog $(-2)$.

Solution:

$(f o g)(-2)=f(g(-2))$

$=f\left(1-(-2)^{2}\right)$

$=f(-3)$

$=(-3)^{2}+(-3)+1$

$=9-3+1$

$=7$