Advertisements
Advertisements
प्रश्न
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
उत्तर
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
x – x2 ≥ 0
∴ x2 – x ≤ 0
∴ x(x – 1) ≤ 0
∴ 0 ≤ x ≤ 1 ...(i)
5 – x ≥ 0
∴ x ≤ 5 ...(ii)
Intersection of intervals given in (i) and (ii) gives
Solution set = [0, 1]
∴ Domain = [0, 1]
APPEARS IN
संबंधित प्रश्न
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
If f(x) = (x − a)2 (x − b)2, find f(a + b).
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
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:
(vi) \[2f - \sqrt{5} g\]
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 \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
If f(x) = cos (log x), then the value of f(x) f(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is
Let f(x) = |x − 1|. Then,
The range of f(x) = cos [x], for π/2 < x < π/2 is
If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to
If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to
Let f(x) = x, \[g\left( x \right) = \frac{1}{x}\] and h(x) = f(x) g(x). Then, h(x) = 1
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is
f is a real valued function given by \[f\left( x \right) = 27 x^3 + \frac{1}{x^3}\] and α, β are roots of \[3x + \frac{1}{x} = 12\] . Then,
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
If f(m) = m2 − 3m + 1, find f(−3)
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Find the domain and range of the following function.
f(x) = `sqrt((x - 3)/(7 - x))`
Express the following logarithmic equation in exponential form
log10 (0.001) = −3
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
Select the correct answer from given alternatives.
If log10(log10(log10x)) = 0 then x =
The equation logx2 16 + log2x 64 = 3 has,
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3
Answer the following:
Find the domain of the following function.
f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - 3) + 1/(log(5 - x))`
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(x))`
Answer the following:
Find the range of the following function.
f(x) = [x] – x
Given the function f: x → x2 – 5x + 6, evaluate f(2)
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
If f(x) = 5x - 3, then f-1(x) is ______
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
Find the range of the following functions given by `|x - 4|/(x - 4)`
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
