If for all real numbers 'x', f(x+1) + f(x-1) = f(x), then what is the value of f(50) + f(47)?
correct answer:- 4
Let $$f(x)$$ be a function satisfying $$f(x)f(y) = f(xy)$$ for all real x, y. If $$f(2) = 4$$, then what is the value of $$f(\frac{1}{2})$$?
correct answer:- 2
Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is:
correct answer:- 5
Find the sum $$\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}} +....+ \sqrt{1+\frac{1}{2007^2}+\frac{1}{2008^2}}$$
correct answer:- 1
Let f(x) = max(2x+3,6-x). Then what is the minimum value of f(x)?
correct answer:- 3
A function $$f(x)$$ is defined as $$f(x, y, z) = xyz - (x + y + z)$$. If it is known that x, y and z are integers such that their absolute values are not equal and $$-12 \leq x, y, z \leq 12$$. Find the maximum value of the function.
correct answer:- 1
Let S be the set of all pairs (i, j) where 1 <= i < j <= n, and n >= 4 (i and j are natural numbers). Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise.
For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.
For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?
correct answer:- 4
Let $$a_1= p$$ and $$b_1 = q$$, where p and q are positive quantities.
Define $$a_n = pb_{n-1} , b_n = qb_{n-1}$$ , for even n > 1. and $$a_n = pa_{n-1} , b_n = qa_{n-1}$$ , for odd n > 1.
Which of the following best describes $$a_n + b_n$$ for even n?
correct answer:- 2
Let $$f(x) = ax^2 + bx + c$$, where a, b and c are certain constants and $$a \neq 0$$?
It is known that $$f(5) = - 3f(2)$$ and that 3 is a root of $$f(x) = 0$$.
What is the other root of f(x) = 0?
correct answer:- 2
Let $$f(x) = ax^2 + bx + c$$, where a, b and c are certain constants and $$a \neq 0$$?
It is known that f(5) = - 3f(2). and that 3 is a root of f(x) = 0.
What is the value of a + b + c?
correct answer:- 5
Let S be the set of all pairs (i, j) where 1 <= i < j <= n, and n >= 4 (i and j are natural numbers). Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise.
For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.
For general n, how many enemies will each member of S have?
correct answer:- 4
Consider the formula, $$S = \frac {a*w}{t + p*w}$$ where a,w,t and p are all positive integers. If 'w' is increased and 'a' , 't' and 'p' are kept constant, then S:
correct answer:- 1
Related Articles for Algebra
