Question

The range of $f$ defined by $f\left(x\right)=\{\begin{array}{cc}{x}^2& x<0\\ x& 0\le x\le 1\\ \frac{1}{x}& x>1\end{array}$ is

• A. $[0,1)$
• B. $[0,2]$
• C. $[0,\infty )$
• D. $[0,4)$

Answer 1

The correct option is C $[0,\infty )$

$f\left(x\right)=x^2,x<0$
Range of $f\left(x\right)$ is $(0,\infty )$
$f\left(x\right)=x,0\le x\le 1$
Range of $f\left(x\right)=0$
$f\left(x\right)=\frac{1}{x};x>1$
Range of f(x) is $(0,1)$.
$\therefore$ range of f is $[0,\infty ).$