7.
Let N be the set of natural numbers and the function f: N N be defined by f(x)=2x+3
yn € N then f is
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12th
Maths
Relations and Functions
Types of Functions
The function f : N → N, N b...
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Asked on December 26, 2019 by
Tejaswi Sangolli
The function f:N→N, N being the set of natural numbers, defined by f(x)=2x+3 is.
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ANSWER
We know that,
f(x)=2x+3
now,
f
′
(x)=2>0 for all x
hence f(x) in always increasing function hence is injective
and for surjective
consider x
1
<x
2
lets consider f(x
1
)<f(x
2
)
2(x
1
)+3<2(x
2
)+3
hence we get x
1
<x
2
hence function is surjective as well
the final results are
f(x) is a injective and surjective function as well
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