Question

If $f:[0,1]\to [-1,3]$ is defined by $f\left(x\right)=x^2+x+1,$ then $f$ is

• A. a many-one function
• B. a one-one function
• C. an onto function
• D. a bijective function

Answer 1

The correct option is B a one-one function

$f\left(x\right)=x^2+x+1$
$f\left(x\right)={(x+\frac{1}{2})}^2+\frac{3}{4}$
Clearly, vertex is at $(-\frac{1}{2},\frac{3}{4})$
So, $f$ is a one-one function in given interval $[0,1]$
Also, $f\left(0\right)=1$ and $f\left(1\right)=3$
$\therefore$ Range is $[1,3]$
Clearly, range is not same as co-domain.
So, given function is an into function.