CAT QA FUNCTION GRAPHS QUESTIONS

Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f (a) = b. Then, the total number of such functions f is

Suppose f(x, y) is a real-valued function such that f(3x + 2y, 2x - 5y) = 19x, for all real numbers x and y. The value of x for which f(x, 2x) = 27, is

If f(x+y) = f(x) f(y) and f(5) = 4, then f(10) - f(-10) equals

Let f(x) = x^2 + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is

If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals [TITA]

For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals [TITA]

Let f(x)=max{5x, 52 - 2x2}, where x is any positive real number.Then the minimum possible value of f(x) is (TITA)

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals. [TITA]

Let f(x)=min{2x2, 52 - 5x}, where x is any positive real number.Then the maximum possible value of f(x) is [TITA]

Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]

Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

If f1(x) = x2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is: (TITA)

Find the area bounded by lines x>0,y>0 and 3x+4y<12?

F(x)=ax³+bx+5, F(10) = 100 then what is the value of F(-10)?

Let f be a function for which f(x/3) = x² + x + 1. Find the sum of all values of z for which f(3z) = 7 .

F(x) = (x - 42)(x - 40)(x - 38)……………..(x - 2k), Where k is an integer k21. Find the maximum value of constant term of F(x)?

a. 2²¹ × 21 !

b. 2²⁰ × 21 !

c. 2²⁰ × 20 !

d. Infinite

f(x + y) = f(x)f(y) for all x, y, f(4) = 3 what is f(–8)?

What is the area enclosed in the region defined by y= |x-1| +2 , Line x = 1 , X- axis and Y-axis. ?

The least integral value of k for which (k-1)x²+ k+8x-1>0 for all xER is

A function f, defined on ordered pairs of positive integers, satisfies the following properties for all integers x & y:

f(x, x) = xf(y, x) = f(x, y) and(x + y) f(x, y) = y f(x, x + y)Find f(14, 52).

greater integer value equals less than or equal to x?