Question

Let $f:R\to$ be defined by $f\left(x\right)=\{\begin{array}{cc}x+2& (x\le -1)\\ x^2& (-1\le x\le 1)\\ 2-x& (x\ge 1)\end{array}$ Find the value of $f(-1.75)+f\left(0.5\right)+f\left(1.5\right)$.

• A. $0$
• B. $2$
• C. $1$
• D. $-1$

Answer 1

The correct option is C $1$

For $x\le -1$

$f\left(x\right)=x+2$

$\Rightarrow f(-1.75)=-1.75+2=.25$

For $-1\le x\le 1$

$f\left(x\right)=x^2\Rightarrow f\left(.5\right)={\left(.5\right)}^2=.25$

For $x\ge 1$

$f\left(x\right)=2-x$

$\Rightarrow f\left(1.5\right)=2-1.5=.5$

$f(-1.75)+f\left(.5\right)+f\left(1.5\right)=.25+.25+.5=1$

Option $C$ is correct.