Find whether the following functions are one-one - onto or not - f-R- R defined by f x - x 2 -3 for all x- R

∵ f(x) = x^2 + 3 #160; #160; #160; f:R → ∵ f(±∝) = ∝^2 + 3 → Many one functionAnd Range of f(x) is (3, ∞) ∴ f(x) is int ...

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Definition of Function

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Question

Find whether the following functions are one-one , onto or not :
$f : R \to R$ defined by $f (x) = x^{2} + 3$ for all $x ϵ R$

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f : R \to R

f (x) = 1 + x^{2}

In each of the following cases, state whether the functions is one-one, onto or bijective. Justify answer.
$(i) f : R \to R$ defined by f(x) =3 - 4x.

$f : R \to R$ defined by $f (x) = 1 + x^{2}$ .

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i) $f : R \to R$ defined by $f (x) = 3 - 4 x$

(ii) $f : R \to R$ defined by $f (x) = 1 + x^{2}$

f : R \to R

f (x) = x^{2} - \frac{x^{2}}{1 + x^{2}}

x \in R

f

f : R \to R

f (x) = \frac{x}{x^{2} + 1}

x \in R

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