Advertisements
Advertisements
प्रश्न
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
उत्तर
Given:
Thus,
APPEARS IN
संबंधित प्रश्न
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
- {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
- {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
- {(1, 3), (1, 5), (2, 5)}
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(iv) \[\frac{f}{g}\]
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(viii) \[\frac{5}{8}\]
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
Which one of the following is not a function?
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If f(m) = m2 − 3m + 1, find f(−3)
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
Check if the relation given by the equation represents y as function of x:
x2 − y = 25
If f(m) = m2 − 3m + 1, find f(0)
Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
Find the domain and range of the following function.
f(x) = `sqrt((x - 3)/(7 - x))`
lf f(x) = 3(4x+1), find f(– 3)
Express the following exponential equation in logarithmic form
e2 = 7.3890
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Select the correct answer from given alternatives
If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
35 | 56 |
45 | 65 |
50 | 69.5 |
55 | 74 |
Find the height of a person whose forehand length is 40 cm
Domain of function f(x) = cos–1 6x is ______.
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Find the domain and range of the function f(x) = `1/sqrt(x - 5)`
The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
Range of the function f(x) = `x/(1 + x^2)` is ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.