Let f-R- R be defined be f-x-x-4- then nbsp-f is one-one and ontof may be one-one and ontof is nbsp-one-one but not ontof is neither one-one nor onto

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Byju's Answer

Standard XII

Mathematics

Using Monotonicity to Find the Range of a Function

Let f:R→ R be...

Question

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

f

is one-one and onto

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f

may be one-one and onto

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f

is one-one but not onto

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f

is neither one-one nor onto

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Solution

The correct option is D $f$ is neither one-one nor onto
$f (1) = f (- 1) = 1,$ so $f$ is not one-one.
$f$ cannot take any negative values, so its range cannot be equal to $R$ , so $f$ is not onto

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Similar questions

Let $f : R \to R$ be defined as $f (x) = x^{4}$ . Choose the correct answer.
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(d) f is neither one-one nor onto

Let f: R → R be defined as f(x) = x⁴. Choose the correct answer.

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Let f:R→R be defined be f(x)=x4, then

The correct option is D f is neither one-one nor ontof(1)=f(−1)=1, so f is not one-one. f cannot take any negative values, so its range cannot be equal to R, so f is not onto

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

The correct option is D $f$ is neither one-one nor onto
$f (1) = f (- 1) = 1,$ so $f$ is not one-one.
$f$ cannot take any negative values, so its range cannot be equal to $R$ , so $f$ is not onto