Function questions
503 published questions with worked solutions.
- Let f: R → R be defined by f(x) = x 1 + x^2 , x ∈ R. Then the range of f is:
- Let N be the set of natural numbers and two functions f and g be defined as f, g: N → N such that f(n) = cases n+1 2 ; & if n is...
- If the domain of the function f(x) = x^2 - 25 (4 - x^2) + _ 10 (x^2 + 2x - 15) is (−∞, α) ∪ [β, ∞), then α² + β³ is equal to:
- Let f : R → R and g : R → R be defined as f(x) = cases _e x, & x > 0 e^ -x , & x 0 cases and g(x) = cases x, & x 0 e^x, & x < 0...
- Consider the function f : R → R defined by f(x) = 2x 1 + 9x^2 . If the composition of f, (f∘f∘f∘…∘f)(x) (10 times) = 2^ 10 x 1 +...
- Let f, g : R → R be defined as: f(x) = |x − 1| and g(x) = cases e^x, & x 0 x + 1, & x 0 cases . Then the function f(g(x)) is
- The function f(x) = x^2 + 2x - 15 x^2 - 4x + 9 , x ∈ R is
- If g(x)=x^2+x-1 and (g f)(x)=4x^2-10x+5, then f ( 5 4 ) is equal to:
- The inverse function of f(x)= 8^ 2x -8^ -2x 8^ 2x +8^ -2x , x (-1,1), is ______________ -
- Let f:(1,3) R be a function defined by f(x)= x[x] 1+x^2 , where [x] denotes the greatest integer x. Then the range of f is :
- Let f(x) = 1 7 - 5x be a function defined on R. Then the range of the function f(x) is equal to:
- Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f : A → ℤ be the...
- Let A = a, b, c and B = 1, 2, 3, 4 . Then the number of elements in the set C = f : A → B | 2 ∈ f(A) and f is not one-one is...
- Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x))=8x^2-2x and g(f(x))=4x^2+6x+1, then the...
- The number of functions f : 1, 2, 3, 4 → a, b, c , which are not onto, is:
- For the function f : [1, ∞) → [1, ∞) defined by f(x) = (x−1)⁴ + 1, among the two statements: (I) The set S = x ∈ [1, ∞) : f(x) =...
- Let f : ℝ → ℝ be defined as f(x)= 2x^2-3x+2 3x^2+x+3 . Then f is:
- Let the range of the function f(x) = 1 2 + 3x + 3x , x ∈ ℝ be [a, b]. If α and β are respectively the A.M. and the G.M. of a and...
- The function f : N – 1 → N; defined by f(n) = the highest prime factor of n, is:
- If f(x) = cases 2 + 2x, & -1 x < 0 1 - x3, & 0 x 3 cases ; g(x) = cases -x, & -3 x 0 x, & 0 < x 1 cases , then range of (fog)(x)...
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