Let f: R arrow R be defined by f(x)=x^4 , then

Correct answer: (D) f is neither one-one nor onto. Given that, f: R arrow R and f(x)=x^4 Since, f (x_1 )=f (x_2 ) ⇒ x_1=± x_2 So, f(x) is not one-one function. Let y=x^4 ⇒ x=√[4]y or ⇒ y=√[4]χ and ⇒ √[4]x ∉ R So, f(x) is not onto function.

Q75 / 180 · KCET 2017 · Mathematics

Let $ f: R \rightarrow R $ be defined by $ f(x)=x^{4} $, then

A
$ \mathrm{f} $ is one-one and onto
B
$ \mathrm{f} $ may be one-one and onto
C
$ \mathrm{f} $ is one-one but not onto
Correct answer
D
$ \mathrm{f} $ is neither one-one nor onto

Solution

Given that, $f: R \rightarrow R$ and $f(x)=x^{4}$ Since, $f\left(x_{1}\right)=f\left(x_{2}\right)$ $\Rightarrow x_{1}=\pm x_{2}$ So, $f(x)$ is not one-one function. Let $y=x^{4}$ $\Rightarrow x=\sqrt[4]{y}$ or $\Rightarrow y=\sqrt[4]{\chi}$ and $\Rightarrow \sqrt[4]{x} \notin R$ So, $f(x)$ is not onto function.

Hence, the correct answer is option: 'D'.

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