The function y = f(x), ,f ,: ,R R , given by f(x) = x | x | + x^3… - Vidyadip

MCQ

The function $y = f(x),\,f\,:\,R \to R$ , given by $f(x) = x\left| x \right| + {x^3}\left| x \right|$ is

A
one- one into
✓
one-one onto
C
many one into
D
many one onto

✓

Answer

Correct option: B.

one-one onto

b
$f(x)=\left\{\begin{array}{ll}{x^{4}+x^{2}} & {, x \geq 0} \\ {-x^{4}-x^{2},} & {x<0}\end{array}\right.$

$f^{\prime}(x) \geq 0,$ one - one function and range is $R.$

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