Question

If f : R → R, given by f(x) = x² + 3, then find the pre image of 2 under f.
[A] 7
[B] 5
[C] -1
[D] Does not exist.

Answer 1

Given Question :-

If f : R → R, given by f(x) = x² + 3, then find the pre image of 2 under f.

[A] 7

[B] 5

[C] -1

[D] Does not exist

$\red{\large\underline{\sf{Solution-}}}$

Given that, f : R → R, given by f(x) = x² + 3

Now, we have to find the pre - image of 2 under f.

It means, we have to find the value of x such that f(x) = 2

So,

$\rm \: f(x) = 2$

$\rm \: {x}^{2} + 3 = 2$

$\rm \: {x}^{2} = 2 - 3$

$\rm \: {x}^{2} = - 1$

So, it implies there exist no real values of x so that x² = - 1

Therefore, it implies 2 doesn't have any pre - image under f.

Hence, Option [ D ] is correct.

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ADDITIONAL INFORMATION

Important Definition

1. Equal functions :- The two functions f and g are said to be equal iff

(a) Domain of f = Domain of g

(b) Co-domain of f = Co-domain of g

(c) f(x) = g(x) for every value of x belongs to their respective domain.

2. Domain and Co-domain

If f : A → B, then the set A is called the domain of f and set B is called the Co-domain of f.

The set of all f - images of elements of set A is called the Range of f and is a subset of B. It is denoted as f(A).

Answer 2

Given Data :

f : R → R, given by f(x) = x² + 3

To Find : The pre - image of 2 under f.

we have to find the value of x such that f(x) = 2

Solution :

⇒ 2 = x² + 3

⇒ x² = -1

it shows, it implies 2 doesn't have any pre - image under f.

• it implies 2 doesn't have any pre - image under f.

➱ Option [D] is correct answer