## JEE Advanced Archive on Functions Multiple Choice One OR More Correct Type Questions

1. Let f: R → R, g: R → R and h: R → R be differentiable functions such that f(x) = x³ + 3x + 2, g(f(x)) = x and h(g(g(x))) = x for all x in R. Then. {IIT JEE 2016}.

(A) g'(2) = 1/15
(B) h'(1) = 666
(C) h(0) = 16
(D) h(g(3)) = 36

Answer: Options (B) and (C) are the correct choices.

1. Let f(x) = sin(π/6 sin(π/2 sinx)) for all x in R and g(x) = (π/2)sinx for all x in R. Let (fog)(x) = f(g(x)) and (gof)(x) = g(f(x)). Then which of the following options is/are true. {IIT JEE 2015}.

(A) Range of f is [-1/2, 1/2]
(B) Range of fog is [-1/2, 1/2]
(C) Limₓ→₀ f(x)/g(x) = π/6
(D) there is an x in R such that (gof)(x) = 1

Answer: Options (A), (B) and (C) are the correct choices.

1. Let f: (-π/2, π/2) → R be given by f(x) = (log(secx + tanx))³. Then. {IIT JEE 2014}.

(A) f(x) is an odd function
(B) f(x) is a one one function
(C) f(x) is an onto function
(D) f(x) is an even function

Answer: Options (A), (B) and (C) are the correct choices.

1. Let f: (-1, 1) → IR be such that f(cos4θ) = 2/(2 – sec²θ) where θ lies in the interval (0, π/4) U (π/4, π/2). Then the value(s) of f(1/3) is/are. {IIT JEE 2012}.

(A) 1 – √(3/2)
(B) 1 + √(3/2)
(C) 1 – √(2/3)
(D) 1 + √(2/3)

Answer: Options (A) and (B) are the correct choices.

1. If f(x) = cos[π²]x + cos[-π²]x, where [.] denotes the greatest integer function, then. {IIT JEE 1991}.

(A) f(π/2) = -1
(B) f(π) = 1
(C) f(-π) = 0
(D) f(π/4) = 1

Answer: Options (A) and (C) are the correct choices.

1. Let g(x) be a function defined on [-1, 1]. If the area of the equilateral triangle with two of its vertices at (0, 0) and (x, g(x)) is √(3/4), then the function g(x) is. {IIT JEE 1989}.

(A) ±√(1 + x²)
(B) √(1 – x²)
(C) -√(1 – x²)
(D) √(1 + x²)

Answer: Options (B) and (C) are the correct choices.

1. If y = f(x) = (x + 2)/(x – 1), then. {IIT JEE 1984}.

(A) x = f(y)
(B) f(1) = 3
(C) y increases with x for x < 1
(D) f is a rational function of x

## JEE Advanced Archive on Functions Integer / Fill in The Blanks Type Questions

1. Let f: R → R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x)f'(y) + f(y)f'(x) for all x and y in R. Then the value of lnf(4) is. {IIT JEE 2018}.

Answer: the value of lnf(4) is 2.

1. If f(x) is an even function defined in (-5, 5), then four real values of x satisfying the equation f(x) = f((x + 1)/(x + 2)) are. {IIT JEE 1996}.

Answer: four real values of x are (-3 ± √5)/2 and (-1 ± √5)/2

1. If f(x) = sin²x + sin²x(x + π/3) + cosx cos(x + π/3) and g(5/4) = 1, then g(f(x)) is. {IIT JEE 1996}.

1. If x < 0, y < 0, x + y + x/y = 1/2 and (x + y)(x/y) = -1/2, then the value of x and y are. {IIT JEE 1990}.

Answer: the value of x and y are -1/4.

1. These are exactly two distict linear functions _ and _ which map from [-1, 1] to [0, 2]. {IIT JEE 1989}.

Answer: two distict linear functions are x + 1 and -x + 1.

1. If f(x) = sinln((√4 – x²)/(1 – x)), then the domain and range of the function f(x) will be. {IIT JEE 1985}.

Answer: the domain and range of the function f(x) are (-2, 1) and [-1, 1] respectively.

1. The domain of the function f(x) = sin⁻¹(log₂(x²/2)) is given by. {IIT JEE 1984}.

Answer: The domain of the function f(x) is [-2, -1] U [1, 2].

1. The value of the function f(x) = 3sin((√(π²/16) – x²)) lies in the interval. {IIT JEE 1983}.

Answer: The value of the function f(x) lies in [0, 3/√2].

### Audience

This IIT JEE Advanced Archive is designed to help the students who are preparing for the one of the toughest entrance exams wordwide (IIT JEE Advanced). With this archive students will get to know the pattern of questions which are usually ask in the exam.

### Prerequisites

This IIT JEE Advanced Archive demands to have the detail knowledge of the chapter “Real Valued Functions”. The other basic requirement to attempt the questions of this archive is, the students must have solved at least 100 questions of the topic.

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