Question

If $f\left(x\right)=\{\begin{array}{cc}{x}^2-3x+2,& x<2\\ x-3,& x\ge 2\end{array}$
$g\left(x\right)=\{\begin{array}{cc}x-2,& x<3\\ x^2+x+1,& x\ge 3\end{array}$
Then which of the following is/are true

• A. $(f+g)\left(2.5\right)=0$
• B. $\left(fg\right)\left(1\right)=0$
• C. $f\left(g\right(3\left)\right)=9$
• D. $g\left(f\right(2\left)\right)=-3$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $(f+g)\left(2.5\right)=0$
B $\left(fg\right)\left(1\right)=0$
D $g\left(f\right(2\left)\right)=-3$

$f\left(2.5\right)=x-3=-0.5$
$g\left(2.5\right)=x-2=0.5$
$\Rightarrow f\left(2.5\right)+g\left(2.5\right)=-0.5+0.5=0$

$\left(fg\right)\left(1\right)=f\left(1\right)\times g\left(1\right)=0$
$f\left(g\right(3\left)\right)=f\left(13\right)=13-3=10$
$g\left(f\right(2\left)\right)=g(-1)=-3$