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Chapter 1 Relations and Functions Ex 1.2 Solutions

Question - 11 : - Letf: R -> R be defined as f (x)=x4. Choose the correct answer.
(a) f is one-one onto                     (b) f is many-one onto
(c) f is one-one but not onto         (d) f is neither one-one nor onto

Answer - 11 : - f: R → R is defined as

Let x, y ∈ R such that f(x) = f(y).

∴does not imply that

For instance,

∴ f is not one-one.

Consideran element 2 in co-domain R. It isclear that there does not exist any x indomain R such that f(x)= 2.

∴ f is not onto.

Hence,function f is neither one-onenor onto.

Thecorrect answer is D.

Question - 12 : - Letf: R –> R be defined as f (x)=3x. Choose the correct answer.
(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto

Answer - 12 : -

f:R –> R is defined by f (x) = 3x
(a) f(x1) = 3x1, f(x2) = 3x2
=> f(x1) = f(x2)
=> 3x1 = 3x2
=> x1 = x2
=> f is one-one
(b) for every member y belonging to co-domain has pre-image x in domain of f.
∵ y = 3x
=>
f is onto
f is one-one and onto. Option (a) is correct.

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