Question

Let R be the set of real numbers and the mapping $f:R\to R$ and $g:R\to R$ be defined by $f\left(x\right)=5-x^2$ and $g\left(x\right)=3\lambda -4$, then the value of $\left(fog\right)(-1)$ is

• A. $-44$
• B. $-54$
• C. $-32$
• D. $-64$

Answer 1

The correct option is A $-44$

Given, $f\left(x\right)=5-x^2,g\left(x\right)=3x-4$
Now, $\left(fog\right)(-1)=f\left\{\begin{array}{c}g(-1)\end{array}\right\}$
$=f(-7)[\because g(-1)=3(-1)-4=-7]$
$=5-(-7{)}^2$
$=-44$