Question

If function $f:R\to [6,\infty )$ is defined by $f\left(x\right)=4x^4+6,$ then $f$ is

[1 mark]

• A. onto only
• B. one-one only
• C. not onto
• D. bijective

Answer 1

The correct option is A onto only

$f\left(x\right)=4x^4+6$

For one-one :
Let $f\left(x_1\right)=f\left(x_2\right)$
$\Rightarrow 4x_1^4+6=4x_2^4+6$
$\Rightarrow x_1=\pm x_2$
$\therefore f$ is many-one function.

Now, $x\in R$
$\Rightarrow x^4\ge 0$
$\Rightarrow 4x^4+6\in [6,\infty )$
Range $=$ Co-domain
$\therefore f$ is onto function.