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hence it is proved f is one one and onto function
I don't know the answer
The function is defined as,
We've to check if it's one - one, onto or both.
A real function is said to be one - one if and only if all elements in has distinct images in i.e.,
Dividing by 2,
This implies is a one - one function.
A real function is said to be onto if and only if the range is the codomain itself, i.e., every elements in have preimages in
Here can accept all real number values without any restriction, hence i.e., range of is the codomain itself.
This implies is an onto function.
Therefore, is both one - one and onto.
one to one if distinct elements in A have
distinct images in B.
A function f from A to B is called
onto if the range of f is equal to B.
as g is 1-1 ,f(a)=f(b)
as f is 1-1 ,a=b
so gof is 1-1
for every gof(x)
as g is onto,there is unique f(x)
as f is onto, there is unique x
so gof is onto
y = 4x - 7 exists.
(ii) let fbe a one-to-one and...