Functions: JEE Questions & Solutions

Let the domain of the function f(x)= 3 [ 5(7- 2(x^2-10x+85)) ] + ^-1 ( 3x-717-x) be (,). Then + is equal to

Let [ ] denote the greatest integer function, and let f(x) = 2 x, x^2. Let S = x (-2,2): the function g(x) = x[x^2] is discontinuous at x.…

Let f(x) = [x]^2 - [x+3] - 3, x R, where [ ] denotes the greatest integer function. Then

Let f and g be functions satisfying f(x+y) = f(x)f(y), f(1) = 7 g(x+y) = g(xy), g(1) = 1, for all x,y N. If x=1^n ( f(x)g(x)) = 19607, then…

Sets A = x Z: ||x-3|-3| 1 and B = x: roots of eq. Number of onto functions A B.

If the domain of the function f(x)= (10x^2-17x+7) (18x^2-11x+1) is (-,a) (b,c) (d,)- e, then 90(a+b+c+d+e) equals

Let f be a function such that 3f(x)+2f ( m19x)=5x, x 0, where m= i=1^9 i^2. Then f(5)-f(2) is equal to

Let f be a polynomial function such that f(x^2+1)=x^4+5x^2+2, for all x R. Then 0^3 f(x) dx is equal to:

Given below are two statements: Statement I: The function f: R R defined by f(x)= x1+|x| is one-one. Statement II: The function f: R R…

Let the range of the function f(x) = 6 + 16 x ( 3 - x) ( 3 + x) 3x 6x, x R be [, ]. Then the distance of the point (,) from the line 3x +…

Let f: R - 0 R be a function such that f(x) - 6f ( 1x) = 353x - 52. If x 0 ( 1 x + f(x)) =, then, R, and + 2 is equal to:

Let f(x) = 2^x+2 + 162^2x+1 + 2^x+4 + 32. Then the value of 8 ( f ( 115) + f ( 215) + + f ( 5915)) is equal to:

The function f: (-,) (-, 1), defined by f(x) = 2^x - 2^-x2^x + 2^-x is:

The sum of all local minimum values of the function f(x) as defined below is: f(x)= arrayll1-2x & if x<-1 13(7+2|x|) & if -1 x 2…

If f(x) = 2^x2^x + 2, x R, then k=1^81 f ( k82) is equal to:

Let f: R R be a function defined by f(x) = ( 2 + 3a)x^2 + ( a+2a-1)x + b, a 1. If f(x + y) = f(x) + f(y) + 1 - 27xy, then the value of 28…

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = ^-1(2[x] + 1) is:

Let f: [0, 3] A be defined by f(x) = 2x^3 - 15x^2 + 36x + 7 and g: [0,) B be defined by g(x) = xx^2025 + 1. If both functions are onto and…

If the domain of the function 5(18x - x^2 - 77) is (,) and the domain of the function (x-1) ( 2x^2 + 3x - 2x^2 - 3x - 4) is (,), then ^2 +…

If the domain of the function f(x) = 1 10 + 3x - x^2 is (a, b), then (1 + a)^2 + b is equal to:

If the domain of the function f(x) = e ( 2x-35+4x) + ^-1 ( 4+3x2-x) is [, ], then ^2 + 4 is equal to

Let the domain of the function f(x) = 2 4 6 (3 + 4x - x^2) be (a, b). If 0^a+b [x^2] dx = p - q r, p, q, r N, (p, q, r) = 1, where [.] is…

Let f be a function such that f(x) + 3f ( 24x) = 4x, x 0. Then f(3) + f(8) is equal to

If the domain of the function f(x) = 7(1 - 4(x^2 - 9x + 18)) is (,) (,), then + + + is equal to

Let f: R R be a continuous function satisfying f(0) = 1 and f(2x) - f(x) = x for all x R. If n f(x) - f ( x2^n) = G(x), then r=1^10 G(r^2)…

Let the domain of the function f(x) = ^-1 ( 4x + 53x - 7) be [, ] and the domain of g(x) = 2 ( 2 - 6 2 ( 2x + 5)) be (,). Then |7( +) + 4(…

The function f: N - 1 N defined by f(n) = highest prime factor of n, is:

If the domain of the function f(x) = ^-1 ( 2 - |x|4) is [-,) -, then + + is equal to:

If the domain of the function f(x) = e ( 2x + 34x^2 + x - 3) + ^-1 ( 2x - 1x + 2) is (, ], then the value of 5 - 4 is equal to:

If the domain of the function f(x) = ^-1 ( 2 - |x|4) + ( e(3 - x))^-1 is [-,) -, then + + is equal to:

Let A = 1,2,3,,7 and let P(A) denote the power set of A. If the number of functions f: A P(A) such that a f(a), a A is m^n, and m and n are…

The function f(x) = x^2 + 2x - 15x^2 - 4x + 9 is:

Let the range of the function f(x) = 12 + (3x) + (3x), where x R and x [a, b]. If and are respectively the A.M. and G.M. of a and b, then /…

If f(x) = 2^2x2^2x + 2, x R, then f ( 12023) + f ( 22023) + + f ( 20222023) is equal to:

Let S = [0, 2): () + () = 0. Then S ^2 ( + 4) is equal to:

Let f(x) = 2x^n +, where R and n N. Given that f(4) = 133 and f(5) = 255, Then the sum of all the positive integer divisors of f(3) - f(2)?

The number of functions f: 1, 2, 3, 4 a Z: |a| 8 satisfying f(n) + 1n f(n+1) = 1, for n 1, 2, 3 is:

Let f: R R be a function defined by f(x) = m ( 2( x - x) + m - 2), for some m, such that the range of f is [0, 2]. Then the value of m is:

The domain of f(x) = x+1(x - 2) / e^2 x x - (2x + 3), x R is:

Let f: R R be a function such that f(x) = x^2 + 2x + 1x + 1

Suppose f is a function satisfying f(x + y) = f(x) + f(y) for all x, y N and f(1) = 15. If the sum from n = 1 to m of [ f(n)n(n + 1)(n + 2)…

Let f: R R be a differentiable function that satisfies the relation f(x + y) = f(x) + f(y) - 1 for all x, y R. If f'(0) = 2, then |f(-2)|…

Suppose f: R (0,) be a differentiable function such that 5f(x + y) = f(x) f(y), x, y R. If f(3) = 320, then n=0^5 f(n) is equal to:

The range of the function f(x) = 3 - x + 2 + x is:

Let A = 1, 2, 3, 5, 8, 9. Then the number of possible functions f: A A such that f(m n) = f(m) f(n) for every m, n A with m n A is equal to

If the domain of the function f(x) = x 1 + x^2, where x is the greatest integer less than or equal to x, is [2, 6), then its range is:

Let f: R 2, 6 R be the real-valued function defined as f(x) = x^2 + 2x + 1x^2 - 8x + 12. Then the range of f is:

Let f: R - 0, 1 R be a function such that f(x) + f ( 11-x) = 1 + x. Then f(2) is equal to:

Let f(x) = x1+x^n, x R - -1, n N, n 2. If f^n(x) = n(f(f( f(x))))(x), then n 0^1 x^n-2 (f^n(x)) dx is equal to:

Let a, b, c be three distinct positive real numbers such that (2a)^ e a = (bc)^ e b and b 2 (e^a) = a e (c). Then 6a + 5bc is equal to:

If the domain of the function f(x) = ^-1 ( 2x5x + 3) is [, ] (,), then |3 + 10( +) + 21 | is equal to:

The domain of the function f(x) = 1 x ^2 - 3 x - 10, where x denotes the greatest integer less than or equal to x, is:

Let A = 1, 2, 3, 4, 5 and B = 1, 2, 3, 4, 5, 6. Then the number of functions f: A B satisfying f(1) + f(2) = f(4) - 1 is equal to.

The number of points where the curve f(x) = e^8x - e^6x - 3e^4x - e^2x + 1, x R cuts the x-axis, is equal to.

Let D be the domain of the function f(x) = ^-1 ( 3x ( 6 + 2 3 x-5x)). If the range of the function g: D R defined by g(x) = x - x, where x…

For the differentiable function f: R - 0 R, let 3f(x) + 2f ( 1x) = 1x - 10, then | f(3) + f ( 14) | is equal to:

If the domain of the function f(x)= e(4x^2+11x+6)+ ^-1(4x+3)+ ^-1 ( 10x+63) is (,), then 36| + | is equal to