12.how to find whether a function is onto or one-one

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Find whether the following functions are one-one or many-one and into or onto if $f : D \to R$ where D is a domain.
i) $f (x) = \frac{3 x^{2}}{4 π} - c o s π x$

Q. 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

Q. State whether the function

f : R \to R

defined by

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

is one-one onto or bijective.

What is the greatest integer function and an onto function?How to determine whether a function is an onto function or not?

Q. Let A = [

-

1, 1]. Then, discuss whether the following functions from A to itself are one-one, onto or bijective:

(i) f(x) =

\frac{x}{2}

(ii) g(x) = |x| (iii) h(x) = x² [NCERT EXEMPLAR]

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