Let f - R - R be a mapping- such that f x - x 2-1- x 2 Then- f isA- Many - one intoB- One - oneC- OntoD- Into

The correct option is A Many – one intof : R → R, where f(x) is x^2/1+x^2 ⇒ f is many one. As, f ( x) = f (x) and range of f(x) ϵ [0, 1) ⊏ codomain. ∴ f is ...

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Standard IX

Mathematics

Many One Function

Let f : R → R...

Question

Let $f : R \to R$ be a mapping, such that $f (x) = \frac{x^{2}}{1 + x^{2}}$ Then, f is

Many – one into

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One – one

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Into

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Onto

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Solution

The correct option is A Many – one into
$f : R \to R$ , where $f (x) i s \frac{x^{2}}{1 + x^{2}}$
$\Rightarrow$ f is many - one.
As, $f (- x) = f (x)$ and range of $f (x) ϵ [0, 1) ⊏$ codomain.
$∴$ f is into.
Hence many – one into

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Let f:R→R be a mapping, such that f(x)=x21+x2 Then, f is

The correct option is A Many – one intof:R→R, where f(x)isx21+x2 ⇒ f is many - one. As, f(−x)=f(x) and range of f(x)ϵ[0,1)⊏ codomain. ∴ f is into. Hence many – one into

Let $f : R \to R$ be a mapping, such that $f (x) = \frac{x^{2}}{1 + x^{2}}$ Then, f is

The correct option is A Many – one into
$f : R \to R$ , where $f (x) i s \frac{x^{2}}{1 + x^{2}}$
$\Rightarrow$ f is many - one.
As, $f (- x) = f (x)$ and range of $f (x) ϵ [0, 1) ⊏$ codomain.
$∴$ f is into.
Hence many – one into