Composite Function
Trending Questions
Q. if x = 1/3 - root 5. then find the value of root x + 1/root x
Q.
Let and be differentiable function satisfying , and Then is equal to
none of these
Q. If the each of algebraic expressions (lx^2) + (mx) + n , (mx^2) + (nx) + l and (nx^2) + (lx) + m are perfect squares , then (l+m)/n = _____ (a)-4 (b)6 (c)-8 (d)none of these
Q. FIND A FOURTH DEGREE EQUATION WITH RATIONAL COEFFICIENTS, ONE OF WHOSE ROOTS IS (√3 + √7)
Q. The set of value of lamda for which the equation x^3 - 3x + lamda = 0 has three distinct real roots, is
Q. Let exactly one root of the equation ax^2+bx+c=0 lies between (0, 1). Then prove that c(a+b+c)<0
Q. Find the value of k for which the quadratic equation 4x^2 - 2kx + k=0 has real and equal roots.
Q. IF a, b, c are in G.P, then discuss the nature of roots of the equations ax^2 + 2bx +c = 0 and ax^2 + 2bx + 2c = 0.
Q.
In a composite function f [g(x)], the following condition must be true
Range of f(x) = Range of g(x)
None of these
Range of g(x) ⊆ domain of f(x)
Range of f(x) ⊆ domain of g(x)
Q.
Let f(x)=x2 and g(x)=sinx for all x∈R. Then the set of all x satifying (f∘g∘g∘f)(x)=(g∘g∘f)(x), where (f∘g)(x)=f(g(x)), is
±√nπ, n∈0, 1, 2, ...
±√nπ, n∈1, 2, ...
π2+2nπ, n∈...−2, 1, 0, 1, 2...
2nπ, n∈...−2, −1, 0, 1, 2, ....
Q. If f(x) = 2x2−5x+1 and g(x) = −x3−x2−3x+2, find g(x) - f(x).
- −x3−x2+2x+1
- −2x3−5x2+5x+1
- −2x3−3x2+2x−4
- −x3−3x2+2x+1
Q.
Let f(x)={1+x, 0≤x≤23−x, 2<x≤3 then f{f(x)}=
none of these
⎧⎪⎨⎪⎩2+x, 0≤x≤12−x, 1<x≤24−x, 2<x≤3
{2+x, 0≤x≤24−x, 2<x≤3
{2+x, 0≤x≤22−x, 2<x≤3
Q. if x+1/3-root 5, then the value of (root x + 1/root x ) is:
Q. What is the domain of the function, f = {(1, 2), (2, 3), (4, 5)}?
- {1, 2, 5}
- {1, 2, 3}
- {2, 3, 5}
- {1, 2, 4}
Q. If p, q, r are the roots of the equation ax^3 + bx^2 + cx + d = 0. then find equation whose roots are
a] pq, qr, pr
b] [pq]^2, [qr]^2, [pr]^2
c] p[q+r], q[p+r], r[p+q]
d] pq+1/r, qr+1/p, pr+1/q
e] p-1/qr, q-1/rp, r-1/pq
Q. If x=1/3-√5 , then the value of (√x+1/√x) is
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. Let f(x)=−1+|x−1|, 1≤x≤3 and g(x)=2−|x+1|, −2≤x≤2, then (fog)(x) is equal to
- {x−1−2≤x≤0x+ 0<x≤2
- {−1−x−2≤x≤0x−1 0<x≤2
- {x+1−2≤x≤0x−1 0<x≤2
- None of these
Q. If f:R→R and g:R→R are given by f(x) = |x| and g(x) = [x], then g(f(x))≤f(g(x) is true for -
- Z∪(−∞, 0)
- (−∞, 0)
- Z
- R
Q.
If (3x)log3=(4y)log4 and (4)logx=(3)logy, then x equals
1/3
1/2
1/4
7
Q. The ratio of the roots of the equation x2 – 5x + a = 0 is same as the ratio of the roots of the equation x2 – 9x + b = 0. If D1 and D2 are the discriminants of the equation x2 – 5x + a = 0 and x2 – 9x + b = 0 respectively, then D1 : D2 is
Q. the seet of values of x satiesfying (x^2 - x -1) (x^2 - x - 7) < -5 is (a, b) uniton (c, d) then a+b+c+d is equal to
Q. Given, f(x) = log1+x1−x and g(x) =3x+x31+3x2 then (fog) (x) equals
- -f(x)
- 3f(x)
- None of these
- [f(x)]3
Q. If f′(x)=3x2+5 and f(0)=−1 , then f(x)=
- x3+5x−1
- Both (a) and (b)
- None
- x3+5x+1
Q. Rationalize the denominator 1/ root 7− root 6 , 1/ root 5 +root 2 , 1 / root 7 − root 2 and 2/ root 3 −root 5 .
Q. 1logxy xyz+1logyz xyz+1logzx xyz=
- 1
- 2
- logzx xyz
- 0
Q. If x= 1/3-root 5 than find the value of root x + 1/ root x
Q. The binomial of degree 20 in the following is:
- x20+1
- x2+20
- 20x+1
- x20+1