Question

MTW
Page No
YOU
Date:
(
then find
the value
of
If f(x) = f(-x) then
=
Sf
o
2 (n) dr.​

Answer 1

Answer:

correct answer b

Step-by-step explanation:

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Class 11

>>Maths

>>Relations and Functions

>>Algebra of Real Functions

>>If f(x) + 2f(1 - x) = x^2 + 2 ; ∀ x ∈ R

Question

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If f(x)+2f(1−x)=x

2

+2; ∀x∈R, then f(x) is given by

Hard

Solution

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Correct option is B)

⇒f(x)+2f(1−x)=x

2

+2⋯⋯(i)

Put x=1−x

⇒f(1−x)+2f(x)=(1−x)

2

+2

Multiply by 2

⇒2f(1−x)+4f(x)=2(1−x)

2

+4⋯⋯(ii)

Subtract (ii) from (i)

−3f(x)=x

2

−2−2(1−x)

2

−3f(x)=x

2

−2−2x

2

+4x

−3f(x)=−(x

2

−4x+4)

f(x)=−

3

(x−2)

2