# IPMAT Question Paper 2019 | IPM Indore Quants

###### IPMAT Sample Paper | IPMAT Question Paper | Question 3

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

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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"

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