Let - be the set of real numbers- If f- is a function defined by fx-x4- then f is

Given : f(x)=x^4 It is an even degree polynomial. nbsp; So,f(x) is many one function. nbsp; Also range of f(x) is [0,∞) which is subset of ℝ(co domain) So,f ...

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Standard XII

Mathematics

Linear Functions

Let ℝ be the ...

Question

Let $R$ be the set of real numbers. If $f : R \to R$ is a function defined by $f (x) = x^{4}$ , then $f$ is

an injective function but not a surjective function

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a surjective but not an injective function

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a bijective function

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Neither an injective nor a surjective function

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Solution

The correct option is D Neither an injective nor a surjective function
Given : $f (x) = x^{4}$
It is an even degree polynomial.
So, $f (x)$ is many-one function.
Also range of $f (x)$ is $[0, \infty)$ which is subset of $R$ (co-domain)
So, $f (x)$ is into function
$∴$ $f$ is neither an injective nor a surjective function.

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Linear Functions

Standard XII Mathematics

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Let R be the set of real numbers. If f:R→R is a function defined by f(x)=x4, then f is

The correct option is D Neither an injective nor a surjective functionGiven : f(x)=x4 It is an even degree polynomial. So,f(x) is many-one function. Also range of f(x) is [0,∞) which is subset of R(co-domain) So,f(x) is into function ∴ f is neither an injective nor a surjective function.

Let $R$ be the set of real numbers. If $f : R \to R$ is a function defined by $f (x) = x^{4}$ , then $f$ is