17 Questions
What is the range of the function f(x) = 2x^3 – 15x^2 + 36x + 1?
[1, 29]
Let f(x) = x^3 + 3x^2 + 4x + bsinx + c cos x, x ∈ R. What can be said about the value of b^2 + c^2?
≥ 1
What type of function is f(x) = x, x ≥ -1?
One-one and onto
Let f(x) = sin(π[x]/2), x ∈ R. What type of function is f(x)?
Periodic
What is the number of onto functions from E = {1, 2, 3, 4} to F = {1, 2}?
8
Let f(x) = ax^2 + bx + c, x ∈ [0, 2]. If f is a bijective function, what is f(2)?
1
Let f(x) = sin^(-1)x^2 + [{n{x}}] + tan^(-1) ( 3 + 2x^2 ), where [.] and {.} are G.I.F. and F.P.F. respectively. What is the number of integers in the range of f?
5
If f : R → S defined by f(x) = sin x – 3 cos x + 1, is onto, then what is the interval of S?
[–1, 1]
Let f(x) = sin([x]π) where [x] denotes the integral part of x. What is the nature of function f?
f is not one-one and non-constant
The function f : [–1, 1] → [–π/2, π/2] defined by f(x) = sin^(-1)x is:
one-one onto
Let f : R → R be a function such that f(x) = x^3 + x^2 + 3x + sin x. What is the nature of function f?
f is one-one and into
Let f : N → N defined by f(x) = x^2 + x + 1, x ∈ N. What is the nature of function f?
one-one but not onto
What is the domain of the function f(x) = 2x - x²?
(-∞, 0) ∪ [2, ∞)
What is the domain of the function y = 2x + 1 / (x - 3x² + 2x³)?
(-∞, 1/2]
What is the domain of the function f(x) = 1 / (x + x² - 2)?
(-∞, -1) ∪ [0, 2)
What is the domain of the function f(x) = 7 - x - 7 / (1 - 5x)?
(-∞, 0) ∪ [2, 3]
What is the domain of the function f(x) = 5 - x - 3 / log₀.₃(x - 1)?
(0, 1) ∪ (1, 2)
Test your understanding of functions, including one-to-one and onto functions, and trigonometric functions like sine. Solve problems and identify the correct properties of functions.
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