Find f x if it satisfies the relation 2 f x - f 1- x - x 2A- x2-2 x-1-3B-C-D- x2-2 x-1-6

The correct option is A x^2+2x 1/3 2f(x)+f(1 x)=x^2 .... (1) Replacing x with (1 x), we get 2f(1 x)+f(x)=(1 x)^2 ....(2) 2 × (1) (2) ⇒ 3f(x) = 2x^2 (1 x) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Definition of Functions

Find f x if i...

Question

Find f(x) if it satisfies the relation

$2 f (x) + f (1 - x) = x^{2}$

$\frac{x^{2} + 2 x - 1}{3}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{x^{2} + 4 x - 1}{6}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{x^{2} + 4 x - 1}{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{x^{2} + 2 x + 1}{6}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$\frac{x^{2} + 2 x - 1}{3}$

$2 f (x) + f (1 - x) = x^{2} . . . . (1)$

Replacing x with (1-x), we get

$2 f (1 - x) + f (x) = (1 - x)^{2} . . . . (2)$

$2 \times (1) - (2) \Rightarrow 3 f (x) = 2 x^{2} - (1 - x)^{2}$

$\Rightarrow f (x) = \frac{x^{2} + 2 x - 1}{3}$

Suggest Corrections

Similar questions

Q. Evaluate

lim x \to 1 \frac{f (x) - f (1)}{x - 1}

where f(x)=

x^{2} - 2 x

Q. If

f (x) = 2 x - 1

, if

x > 1

;

= x^{2} + 1

, if

- 1 \leq x \leq 1

, then

\frac{f (1) + f (3) + f (0)}{f (2) + f (- 1) + f (\frac{1}{2})}

is?

Q. If

f (x) = x^{2} - 2 x + 4

then the set of values of

x

satisfying

f (x - 1) = f (x + 1)

Q. If

(x) = x^{2} - 2 x + 4

then the set of values of

x

satisfying

f (x - 1) = f (x + 1)

Q. Given that

x^{2} f (x) + f (1 - x) = 2 x - x^{4}

Prove that

f (x) = 1 - x^{2}

Join BYJU'S Learning Program

Find f(x) if it satisfies the relation 2f(x)+f(1−x)=x2

The correct option is A x2+2x−13 2f(x)+f(1−x)=x2 ....(1) Replacing x with (1-x), we get 2f(1−x)+f(x)=(1−x)2 ....(2) 2×(1)−(2)⇒3f(x)=2x2−(1−x)2 ⇒f(x)=x2+2x−13

Find f(x) if it satisfies the relation

$2 f (x) + f (1 - x) = x^{2}$

The correct option is A
$\frac{x^{2} + 2 x - 1}{3}$

$2 f (x) + f (1 - x) = x^{2} . . . . (1)$

Replacing x with (1-x), we get

$2 f (1 - x) + f (x) = (1 - x)^{2} . . . . (2)$

$2 \times (1) - (2) \Rightarrow 3 f (x) = 2 x^{2} - (1 - x)^{2}$

$\Rightarrow f (x) = \frac{x^{2} + 2 x - 1}{3}$