Domain
Trending Questions
- (−e, 1)
- (−1, e)
- (1, e)
- (−e, −1)
Let f and g be real functions, defined by f(x)=√x+2 and g(x)=√4−x2. Find
(i) (f+g)(x)
(ii) (f−g)(x)
(iii) (fg)(x)
(iv) (ff)(x)
(v) (gg)(x)
(vi) (fg)(x)
Find the domain of f(2x - 1) if the domain of f(x) is [-1, 1]
[-1, 1]
[0, 1]
[-1, 0]
[1, 2]
- [12, ∞)
- (12, ∞)
- (−∞, ∞)
- (−12, ∞)
If 3sinβ = sin(2α + β), then tan (α + β) is equal to
2tan
2tan
tan
+ tan
None of these
- {3, 4}
- {3, −4}
- {−3, −4}
- the function is defined everywhere
Write the complex number z=i−1cosπ3+i sinπ3 in the polar form.
Solve the following systems of inequalities graphically:
3x+2y≤12, x≥1, y≥2
If |x−3|x−3>0, then
x ϵ (−3, ∞)
x ϵ (3, ∞)
x ϵ [−3, ∞)
x ϵ [3, ∞)
Draw the graph of the greatest integer function:
f:R→R:f(x)=[x] for all xϵR
limx→02x−1(1+x)12−1
- R−{−1±√52}
- R−{−1±√32}
- R−{−1±√72}
- R−{−1±√62}
Identify the function based on the given information.
1. Domain of the function is R+
2. F(x1.x2)=F(x1)+F(x2)
3. F(x1x2)=F(x1)−F(x2)
4. F(1)=0
5. F(2m) is proportional to m.
6. Range of function is R
Logarithm Function
Exponential Function
Absolute value function
- domain of f is R−{√2}
- there are three pre-images of 4
- there is only one pre-image of 4
- domain of f is R−{±√2}
is defined for
None of these
If f(x) = sin log (√4−x21−x), then the domain of f(x) is
(1, 2)
(−2, 1)
(0, 2)
(−1, 2)
(a) x ∈ R
(b) x ∈ Q
(c) x ∈ R − Q
(d) x ∈ R, x ≠ 0
If ax2+bx+c, a, b, cϵR, a < 0 has no real zeros and a - b+c<0, then the
value of ac
> 0
< 0
= 0
< -1