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
GMAT Functions questions test your understanding of how functions work, including plugging values, composition, and inverse functions.
Read carefully, solve the inner function first in cases like f(g(x)), and substitute values step by step to avoid confusion.
Students often misread f(x+1) as f(x)+1, ignore domain restrictions, or forget to reverse functions properly.
No. They mostly test your logical understanding of formulas and substitution, not advanced algebra.
Function composition means combining two functions, written as f(g(x)), where you solve g(x) first, then plug it into f.
Swap x and y in the equation and solve for y again - this gives you the inverse, denoted as f⁻¹(x).
You can download the GMAT Functions Formula PDF linked in this blog to revise key formulas and examples.
Yes, function-based questions are a recurring part of GMAT Quant, especially in algebra and word problem sections.
