IPMAT 2019 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2019 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here:**IPM Sample Paper**

Question 3: A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then the value of f(8) is

Buy CAT'21 95-99 Booster Course for just

Valid until 19th Sep

Online Batches Available Now!

f (x) f (y) = f (2xy + 3) + 3f (x + y) - 3f (y) + 6y

Putting x = y = 0,

f (0) f (0) = f (2.0.0 + 3) + 3f (0 + 0) - 3f (0) + 6.0

f (0)^{2}= f (3) + 3f (0) - 3f (0) + 0

f (3) = f (0)^{2}

Putting y = 0,

f (x) f (0) = f (2.x.0 + 3) + 3f (x + 0) - 3f (0) + 6.0

f (x) f (0) = f (3) + 3f (x) - 3f (0)

f (x) f (0) = f (0)^{2}+ 3f (x) - 3f (0)

f (x) f (0) - f (0)^{2}= 3f (x) - 3f (0)

f (0) * (f (x)- f (0)) = 3 * (f (x)- f (0))

Either f(x) = f(0) or f(0) = 3

Since all functions can’t have the same value, f(0)=3.

Putting x=0, y=3,

f (0) f (3) = f (2.0.3 + 3) + 3f (0 + 3) - 3f (3) + 6.3

f(0) f(3) = f(3) + 3f(3) -3f(3) +18 = f(3) +18.

3 f(3) = f(3) + 18. Therefore, f(3) =9.

f(3) = 9.

Putting x=0, y=8.

f (0) f (8) = f (2.0.8 + 3) + 3f (0+ 8) - 3f (8) + 6.8

3.f(8) = f(3) + f(8) – f(8) + 48

3. f(8) = 9 + 48.

f(8) = 19

The question is**"A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then the value of f(8) is"**

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com