Advertisements
Advertisements
प्रश्न
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
उत्तर
g(x) = x3 − 2x2 − 5x + 6
= (x – 1) (x2 – x – 6)
= (x – 1) (x + 2) (x – 3)
g(x) = 0
∴ (x – 1) (x + 2) (x – 3) = 0
∴ x – 1 = 0 or x + 2 = 0 or x – 3 = 0
∴ x = 1, – 2, 3
APPEARS IN
संबंधित प्रश्न
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
f, g, h are three function defined from R to R as follow:
(ii) g(x) = sin x
Find the range of function.
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
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:
(iii) 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) \[\frac{5}{8}\]
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.
Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}
Find the domain of fg.
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\] is equal to
Check if the following relation is a function.
Check if the following relation is a function.
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
Express the area A of circle as a function of its circumference C.
Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Express the following exponential equation in logarithmic form
e2 = 7.3890
Express the following logarithmic equation in exponential form
ln e = 1
Find the domain of f(x) = ln (x − 5)
If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
Answer the following:
Find x, if x = 33log32
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
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 length of forehand of a person if the height is 53.3 inches
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`
Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The period of the function
f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.
