Function questions
503 published questions with worked solutions.
- If the domain of the function f(x) = ^ -1 ( 2 - |x| 4 ) + ( _e(3 - x) )^ -1 is [−α, β) − γ , then α + β + γ 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...
- If f(x) = 4x+3 6x-4 , x ≠ 2/3 and (fof)(x) = g(x), where g : ℝ − 2/3 → ℝ − 2/3 , then (gogog)(4) is equal to
- The range of the function, f(x)= _ 5 (3+ ( 3 4 +x )+ ( 4 +x )+ ( 4 -x )- ( 3 4 -x ) ) is :
- The inverse of y = 5^ x is :
- Let f(x) = x-2 x-3 . Let g : R R be given as g(x) = 2x – 3. Then, f^ -1 (x)+g^ -1 (x) is equal to :
- The real valued function f(x)= cosec ^ -1 x x-[x] , where [x] denotes the greatest integer less than or equal to x, is defined...
- If the functions are defined as f(x) = x and g(x) = 1-x , then what is the common domain of the following functions : f+g, f–g,...
- Let [x] denote the greatest integer x, where x R. If the domain of the real valued function f(x)= |[x]|-2 |[x]|-3 is (- ,a) [b,c)...
- Let f:R R be defined as f(x) = 2x – 1 and g:R- 1 R be defined as g(x)= x- 1 2 x-1 . Then the composition function f(g(x)) is :
- The coefficient of x^n in the expansion of (1+ x^2 2! + x^4 4! + )^2, when n is odd, is
- Consider function f:A B and g:B C (A, B, C R) such that (gof)^ -1 exists, then:
- Let f(x) = ^ -1 x and g(x) = x^2-x-2 2x^2-x-6 If g(2) = _ x 2 g(x), then the domain of the function fog is
- The domain of the function f(x) = ^ -1 ( x^2-5x+6 x^2-9 ) _e(x^2-3x+2) is -
- Let f : ℝ ℝ be defined by f(x) = x − 1 and g : ℝ − 1, −1 ℝ be defined by g(x) = x^ 2 /(x^ 2 - 1). Then the function f∘g is:
- Let f(x) = x-1 x+1 , x ℝ − 0, −1, 1 . If f^ n+1 (x) = f(f^ n (x)) for all n ℕ, then f^ 6 (6) + f^ 7 (7) is equal to
- Let f:N N be a function such that f(m + n) = f(m) + f(n) for every m, n N. If f(6) = 18, then f(2) (3) is equal to :
- Let the sets A and B denote the domain and range respectively of the function f(x) = 1 [x]-x , where [x] denotes the smallest...
- Let f(x) = x^2 and g(x) = x for all x R . Then the set of all x satisfying (f g g f)(x) = (g g f)(x), where (f g)(x) = f(g(x)), is
- Let f_1 : R R , f_2 : [0, ) R , f_3 : R R and f_4 : R [0, ) be defined by f_1(x) = cases |x| & if x < 0, e^x & if x 0; cases...
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