Advertisements
Advertisements
प्रश्न
Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`
उत्तर
For real value of f
x + |x| > 0
When x > 0,
x + |x| > 0
⇒ x + x > 0
⇒ 2x > 0
⇒ x > 0
When x < 0,
x + |x| > 0
⇒ x – x > 0
⇒ 2x > 0
⇒ x > 0
So, x > 0, to satisfy the given equation.
Therefore, the domain of f = R+
APPEARS IN
संबंधित प्रश्न
Define a function as a correspondence between two sets.
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
The domain of definition of the function \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is
If f(m) = m2 − 3m + 1, find f(−3)
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Find the domain and range of the following function.
f(x) = 7x2 + 4x − 1
Express the area A of a square as a function of its perimeter P
Express the area A of circle as a function of its diameter d
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x2
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
Express the following exponential equation in logarithmic form
3–4 = `1/81`
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}
Answer the following:
Let f: R → R be a function defined by f(x) = 5x3 – 8 for all x ∈ R, show that f is one-one and onto. Hence find f –1
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 f(x) = 3x4 – 5x2 + 7 find f(x – 1)
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
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
A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find `(f/g)(x)`
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.
If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.
