Question

Let $f$ and $g$ be functions from $R$ to $R$ defined as
$f(x)=\{\begin{array}{ll}7x^2+x-8,x\le 1& \\ 4x+5,1<x\le 7& \\ 8x+3,x>7& \end{array}$ and $f(x)=\{\begin{array}{ll}|x|,x<-3& \\ 0,-3\le x<2& \\ x^2+4,x\ge 2& \end{array}$
Then,

• A. $(fog)(-3)=8$
• B. $(fog)(9)=683$
• C. $(gof)(0)=-8$
• D. $(gof)(6)=427$

Answer 1

Answer: (B)

We have $g(-3)=0$
$\Rightarrow f\left(g\left(-3\right)\right)=f\left(0\right)=7{\left(0\right)}^2+0-8$
$=-8$
Now, $g\left(9\right)=9^2+4$
$=85$
$\Rightarrow f\left(g\left(9\right)\right)=f\left(85\right)=8\times 85+3$
$=683$
Also, $f\left(0\right)=7{\left(0\right)}^2+0-8$
$=-8$
$\Rightarrow g\left(f\left(0\right)\right)=g\left(-8\right)=\left|-8\right|=8$
Also, $f\left(6\right)=4\times 6+5$
$=29$
$\Rightarrow g\left(f\left(6\right)\right)=g\left(29\right)={\left(29\right)}^2+4$
$=845$