General Tips for Choosing Function
Trending Questions
If 3f(x)+5f(1x)=1x−3 for all non-zero x, then f(x) =
114(−3x+5x+6)
114(3x+5x−6)
114(−3x+5x−6)
None of these
If x + y = k is normal to the curve y2 = 12x, then k is equal to
-9
-3
9
3
Let f(x)=|x−1|. Then,
f(x+y)=f(x)f(y)
f(x2)=[f(x)]2
f(|x|)=|f(x)|
None of these
- 4052
- 5052
- 6052
- 5250
If f(x) be defined on [-2, 2] and is given by f(x)={−1, −2≤x≤0x−1, 0<x≤2
and g(x)=f(|x|)+|f(x)|. Find g(x).
If f, g, h are real functions defined by f(x)=√x+1, g(x)=1x and h(x)=2x2−3, then find the values of (2f + g - h) (1) and (2f + g - h) (0).
If ef(x)=10+x10−x, xϵ(−10, 10) and f(x)=kf(200x100+x2), then k =
0.8
0.5
0.7
0.6
Let f(x)=x2 and g(x)=2x+1 be two real functions. Find (f + g), (f - g) (x), (fg) (x) and (fg)(x)
If f:R→R be given by f(x)=4x4x+2 for all xϵR. Then,
f(x)=f(1−x)
f(x)+f(1−x)=0
f(x)+f(1−x)=1
f(x)+f(x−1)=1
Let, such that , then find the value of ‘’
If for non-zero x, af(x)+bf(1x)=1x, −5, where a≠b, then find f(x).
Let f:{1, 3, 4} → {1, 2, 5}and g:{1, 2, 5} → {1, 3}be given by f:(1, 2), (3, 5), (4, 1)and g:{(1, 3), (2, 3), (5, 1)}. Write down gof.
Find f + g, f - g, cf(cϵR, c≠0). fg. 1f and fg in each of the following :
(i) f(x)=x3+1 and g(x)=x+1
(ii) f(x)=√x−1 and g(x)=√x+1
- 1
- 2
- 3
- Cannot be found since degree of f(x) is not given
- 12
- 58
- 1724
- 56
If the sum of an infinite G.P, whose first term is 9, is x, then x belongs to
None of these
A function f:R→[1, ∞) satisfies the equation f(xy)=f(x)f(y)−f(x)−f(y)+2. If f is differentiable on R−0 and f(2)=5, f′(x)=f(x)−1x.λ then λ =________
f(1)=1 and f(1)+2f(2)+…+nf(n)=n(n+1)f(n) for n≥2.
If f(1003)=1K, then K equals
- 1003
- 2003
- 2005
- 2006
- k291
- 91k
- 91n
- cannot be determined from the given information
- f(x) is an even function
- f(x) is an odd function
- If f(2)=a, then f(−2)=a
- If f(4)=b, then f(−4)=−b
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f:R→R defined by f(x)=3−4x
(ii) f:R→R defined by f(x)=1+x2
- x
- y
- 0
- x+y2
- ⎧⎨⎩−x, −2≤x≤00, 0<x≤12(x−1), 1<x≤2
- ⎧⎨⎩1, −2≤x≤0−x+1, 0<x≤1x−1, 1<x≤2
- ⎧⎨⎩−x+2, −2≤x≤00, 0<x≤1x−1, 1<x≤2
- ⎧⎨⎩2−2≤x≤000<x≤12(x−1)1<x≤2
If f(x)=4x−x2, xϵR, then write the value of f(a + 1) - (a - 1).