Question

Solve this ques of Jee mains
Chapter → Functions​

Answer 1

EXPLANATION.

If f(x) + 2f(1/x) = 3x, x ≠ 0

⇒ S = {x ∈ R : f(x) = f(-x)} ; then S.

As we know that,

⇒ f(x) + 2f(1/x) = 3x. - - - - - (1).

Put the value of x = 1/x in the equation, we get.

⇒ f(1/x) + 2f(x) = 3(1/x).

⇒ 2f(x) + f(1/x) = 3(1/x). - - - - - (2).

From equation (1) & (2), we get.

Multiply equation (1) by 1, we get.

Multiply equation (2) by , we get.

⇒ f(x) + 2f(1/x) = 3x. - - - - - (1). x 1.

⇒ 2f(x) + f(1/x) = 3(1/x). - - - - - (2). x 2.

We get,

⇒ f(x) + 2f(1/x) = 3x. - - - - - (3).

⇒ 4f(x) + 2f(1/x) = 6/x. - - - - - (4).

Subtract equation (3) & (4), we get.

⇒ f(x) + 2f(1/x) = 3x. - - - - - (3).

⇒ 4f(x) + 2f(1/x) = 6/x. - - - - - (4).

⇒ -      -                -

⇒ - 3f(x) = 3x - 6/x.

⇒ 3f(x) = 6/x - 3x.

⇒ f(x) = 2/x - x.

⇒ f(x) = f(-x).

⇒ 2/x - x = - (2/x - x).

⇒ 2/x - x = - 2/x + x.

⇒ 2/x + 2/x = x + x.

⇒ 4/x = 2x.

⇒ 4 = 2x².

⇒ x² = 2.

⇒ x = ± √2.

S, contains exactly two elements.

Option [B] is correct answer.

Answer 2

Step-by-step explanation:

Given

:- f(x) + 2 f(1/x) = 3x , [ x≠0 ] ______(1)

Replacing , x as 1/x

We have. , f(1/x) + 2f(x) = 3/x

→ 2 f(x)+ f(1/x) = 3/x _______(ii)

On multipling Eq. (ii) by 2 and subtracting Eq. (i)

→ 4f(x) + 2f(1/x) - f(x) -2f(1/x) = 6/x - 3x

• → 3f(x) = 6/x - 3x

• → f(x) = 2/x - x

• Now, consider f(x) = f(-x)

• → 2/x - x = -2/x + x

• → 4/x = 2x

• → 2x² = 4

• → x² = 2

• → x = ±√2

∴ S contains exactly two elements .