Composite Function
Trending Questions
Q.
If is the inverse of a function and, then is equal to
Q.
Prove the following:
sin x - sin 3xsin2x−cos2x=2sin x.
Q. The number of values of k, for which both the roots of the equation x^2-6kx+9(k^2-k+1)=0 are real, distinct and have values almost 3 is
Q.
Explain the concept of composite function with the help of an example.
Q. Iff:R→R be a function satisfying the functional Rule f(x+f(y))=f(x)+x+f(x−y);∀x, y∈R then
Column IColumn II(P)f(0)(A)1(Q)|f(1)+f(2)|(B)3(R)|f(2)+f(−3)|(C)0(S)|f(1)+f(−3)|(D)2
Column IColumn II(P)f(0)(A)1(Q)|f(1)+f(2)|(B)3(R)|f(2)+f(−3)|(C)0(S)|f(1)+f(−3)|(D)2
- P→B, Q→A, R→C, S→D
- P→A, Q→B, R→D, S→C
- P→C, Q→B, R→A, S→D
- P→C, Q→B, R→D, S→A
Q. If 2sin^(-1)x=-sin^(-1)(2x*sqrt(1-x^(2)))-pi_(i) then x satisfies
Q. If f(x)={x, x is rational1−x, x is irrational,
then f(f(x)) is
then f(f(x)) is
- x ∀ x∈R
- f(x)={x, x is irrational1−x, x is rational
- f(x)={x, x is rational1−x, x is irrational
- None of these
Q. The complete set of values of ‘k’ for which both roots of the equation x2 + 3kx + (k – 1) = 0 are less than or equal to 1 is
Options:
(0, ∞)
Should have chosen
[0, ∞)
Wrong
(–∞, 0)
Q. Let there are n number of polynomial functions fi:R→R, i∈N satisfying the equation
f(a+f(a+b))+f(ab)−f(a+b)−bf(a)=a ∀ a, b∈R. Then
f(a+f(a+b))+f(ab)−f(a+b)−bf(a)=a ∀ a, b∈R. Then
- there exists at least one odd function.
- there exists at least one even function.
- fi(1)=1 ∀ i∈N
- n∑i=1fi(x)=k, where k is a constant.
Q. If , then the values of x are
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Q.
In a composite function f [g(x)], the following condition must be true
Range of f(x) = Range of g(x)
Range of g(x) ⊆ domain of f(x)
Range of f(x) ⊆ domain of g(x)
None of these
Q. find x for :
sin^(-1)(x) + 2sin^(-1)(1-x) = (pi/2)
Q. f:(0, ∞)→(0, ∞), f(xf(y))=x2ya(a∈R) then
Value of a is
Value of a is
- 2
- 4
- 6
- 8
Q. If f(x)=sin2x+sin2(x+π3)+cosx cos(x+π3)and g(54)=1, then (gof)(x)=
- -2
- -1
- 2
- 1
Q. f(x)={x−1, −1≤x<0 x2, 0≤x≤1 and g(x)=sinx. Consider the function h1(x)=f(|g(x)|) and h2(x)=|f(g(x))|
Which of the following is not true about h2(x)?
Which of the following is not true about h2(x)?
- Domain is R
- It is periodic function with period 2π
- Range is [0, 1]
- None of these
Q.
sin p = sin q .So, p=?
2nπ + (-1)nq, where n ЄZ
nπ + (-1)nq, where n ЄZ
(2n + 3)π + (-1)nq, where n ЄZ
Q. Int (e^x){(1+sin 2x)/(1-sin 2x)
Q. The value of dy/dx is, when y=f(1/x) and f(x)=sin(x²)
Q. If f(x)=max{1+sinx, 1, 1−cosx}, ∀ x∈[0, 2π] and g(x)=max{1, x−1} ∀ x∈R, then
- g(f(0))=1
- g(f(0))=1
- f(f(1))=1
- f(g(0))=1+sin1
Q. If f(x)={x3+1, x<0x2+1, x≥0, g(x)=⎧⎨⎩(x−1)13, x<1(x−1)12, x≥1 then (gof) (x) is equal to
- x, ∀xϵR
- x−1, ∀xϵR
- x+1, ∀xϵR
- None of these
Q. f(x)={x−1, −1≤x<0 x2, 0≤x≤1 and g(x)=sinx. Consider the function h1(x)=f(|g(x)|) and h2(x)=|f(g(x))|
Which of the following is not true about h2(x)?
Which of the following is not true about h2(x)?
- Domain is R
- It is periodic function with period 2π
- Range is [0, 1]
- None of these
Q.
2sinx
–sinx/2
(sinx/2)