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The domain of the function f(x)= is
The domain of the function f(x) = log_{1/2} is
If q^{2} – 4pr = 0, p > 0, then the domain of the function, f(x) = log (px^{3} + (p + q) x^{2} + (q + r) x + r) is
Find domain of the function f(x) =
The domain of the function is (where [x] denotes greatest integer function)
Range of f(x) = 4^{x} + 2^{x} + 1 is
Range of f(x) = log_{√5} {√2 (sin x –cos x) + 3} is
The range of the functin f(x) = log_{√2}(2– log_{2} (16 sin^{2} x + 1)) is
If f(x) = , then range of f(x) is
The sum is equal to (where [*] denotes the greatest integer function)
Which of the following represents the graph of f(x) = sgn ([x + 1])
If f(x) = 2 sin^{2}q+4 cos (x+q) sin x. sin q+cos (2x+2q) then value of f^{2}(x) + f^{2} is
Let f(x) = ax^{2} + bx + c, where a, b, c are rational and f : Z → Z, where Z is the set of integers. Then a+ b is
f : Z → Z
f(x) = ax^{2} + bx + c
x=0, f(0) = a(0)^{2} + b(0) + c
= c [it is an integer]
x=1, f(1) = a + b+ c should be an integer
a + b+ c = 1
a + b = 1c
a+b should be an integer.
Which one of the following pair of functions are identical ?
The function f : [2, ∞) → Y defined by f(x) = x^{2} – 4x + 5 is both one–one & onto if
Let f : R → R be a function defined by f(x) = then f is
Let f : R → R be a function defined by f(x) = x^{3} + x^{2} + 3x + sin x. Then f is
If f(x) = x^{3} + (a – 3) x^{2} + x + 5 is a one–one function, then
The graph of the function y = f(x) is symmetrical about the line x = 2, then
The function f : R → R defined by f(x) = 6^{x} + 6^{x} is
Let `f' be a function from R to R given by f(x) = . Then f(x) is
If f(x) = cot^{1} x : R^{+} → and g(x) = 2x – x^{2} : R → R. Then the range of the function f(g(x)) wherever define is
g(x) = 2xx^{2}
x(2x)
b/2a =. 2/(2)
=> 1
x implies (0,2)
g(x) implies (0,1]
f(g(x)) = [π/4, π/2)
Let g(x) = 1 + x – [x] and f(x) = , then x, fog(x) equals (where [*] represents greatest integer function).
Let f: [0, 1] → [1, 2] defined as f(x) = 1 + x and g : [1, 2] → [0, 1] defined as g(x) = 2 – x then the composite function gof is
Let f & g be two functions both being defined from R → R as follows f(x) = and g(x) = . Then
If y = f (x) satisfies the condition f = x^{2} + (x > 0) then f(x) equals
It is given that f(x) is an even function and satisfy the relation f(x) = then the value of f(10) is
Fundamental period of f(x) = sec (sin x) is
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99 videos291 docs212 tests
