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Question

Let ‘f’ be a linear function with the properties that $f(1) \underline< f(2), f(3) \underline> f(4) \quad and \quad f(5) = 5.$ Which of the following statements is true?

Possible Answers

Selected	Possible Answer



	@

Question

$If \quad f(x) = ax ^4 - bx ^2 + x + 5 \quad and \quad f(-3) = 2 \quad then \quad f(3) = ?$

Possible Answers

Selected	Possible Answer
	2
	1
	8
	-5

Question

$A \quad function \quad f:Z\rightarrow Z \quad is \quad defined \quad as$
$f(x) = n+3, \quad if \quad n \quad is \quad odd$
$f(x) = \frac{n}{2}, \quad if \quad n \quad is \quad even$
Suppose K is odd and f{f(f(k))}=27. What is the sum of the digits of K?

Possible Answers

Selected	Possible Answer
	8
	7
	5
	6

Question

$If \quad f(x+1) = (x-1) ^2 \quad then \quad find \quad f(x-1)$

Possible Answers

Selected	Possible Answer

Question

$f(x) = 1+x , \quad if \quad 0 \underline< x \underline< 2$
$f(x) = 3-x , \quad if \quad 2 < x \underline< 3, \quad find \quad f[f(3)]$

Possible Answers

Selected	Possible Answer
	2
	1
	3
	0

Question

$f(x) = (1990-x ^2) ^\frac{1}{3}, g(x) = (1990 - x ^3) ^\frac{1}{2}, \quad find \quad fog(x)$

Possible Answers

Selected	Possible Answer
	x
	g(x)
	gof(x)
	f(x)

Question

$f(x) = f(x-1) \quad if \quad x > 0$
$f(x) = |x| \quad if \quad x \underline< 0$ <br/. Find the value of f(2.4) – f(2).

Possible Answers

Selected	Possible Answer
	0.4
	None
	0
	0.6

Question

$If \quad f(m+1) = m(-1) ^{m+1} - 2f(m) \quad for \quad integers \quad m \underline> 1$
$and \quad f(1) = f(2001) \quad then \quad f(1) + f(2) +.......+ f(2000) = ?$

Possible Answers

Selected	Possible Answer
	-1000/7
	1000/3
	1000/7
	-1000/3

Question

$f: R \rightarrow R \ni f(x+f(x)) = 4f(x), \quad f(1) = 4. \quad Find \quad f(5).$

Possible Answers

Selected	Possible Answer
	16
	12
	10
	14

Question

If ‘f’ is defined for all real ‘x’ $f(a+b) = f(ab), \forall a, b \in R, f(-\frac{1}{2}) = - \frac{1}{2}$ then find f(-a ^2)

Possible Answers

Selected	Possible Answer
	-1/4
	-1/8
	-1/2
	1/4

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