Advertisements
Advertisements
प्रश्न
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
उत्तर
f(x) = `sqrt(x) - 3`, g(x) = 5 – x
f(x) = g(x)
∴ `sqrt(x) - 3` = 5 – x
∴ `sqrt(x)` = 5 – x + 3
∴ `sqrt(x)` = 8 – x
On squaring, we get
∴ `(sqrt(x))^2 = ( 8 – x)^2` ...[∴ (a − b)2 = a2 − 2ab + b2]
x = 64 – 16x + x2
∴ 64 – 16x – x + x2 = 0
∴ x2 – 17x + 64 = 0
Factorize or use the quadratic formula:
x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
where a = 1, b = –17, and c = 64
x = `(-(-17) ± sqrt((-17)^2 - 4(64)))/2`
= `(17 ± sqrt(289 - 256))/2`
= `(17 ± sqrt(33))/2`
∴ x = `(17 + sqrt(33))/2` or x = `(17 - sqrt(33))/2`
APPEARS IN
संबंधित प्रश्न
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
Which one of the following is not a function?
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
The domain of definition of \[f\left( x \right) = \sqrt{4x - x^2}\] is
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
Check if the following relation is function:
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(3)
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
Check if the following relation is a function.
Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Find the domain and range of the following function.
f(x) = `sqrt((x - 2)(5 - x)`
Express the following logarithmic equation in exponential form
In `1/2` = – 0.693
Write the following expression as sum or difference of logarithm
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph
Answer the following:
If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy
Answer the following:
Show that, logy x3 . logz y4 . logx z5 = 60
Answer the following:
If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour
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 |
Check if this relation is a function
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(x) = `sqrtx` is ______.
The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f – g)(x)
Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.
