Question

If $f:R\to R,f\left(x\right)=(x+1{)}^2$ and $g:R\to R,g\left(x\right)=x^2+1$ then $\left(fog\right)\left(3\right)$ is equal to

• A. $121$
• B. $144$
• C. $112$
• D. $11$

Answer 1

The correct option is A $121$

Given,

$f:R\to R,f\left(x\right)=(x+1{)}^2$ and $g:R\to R,g\left(x\right)=x^2+1$

$g\left(3\right)=3^2+1=10$

$f\left(10\right)=(10+1{)}^2=121$

$\therefore fog\left(3\right)=f\left(g\right(3\left)\right)=f\left(10\right)=121$

Hence, option A.