Advertisements
Advertisements
प्रश्न
Write the range of the real function f(x) = |x|.
उत्तर
Given:
f (x) = | x |, x ∈ R
We know that
\[\left| x \right| = \begin{cases}x, & x \geq 0 \\ - x & x < 0\end{cases}\]
It can be observed that the range of f (x) = | x | is all real numbers except negative real numbers.
∴ The range of f is [0, ∞) .
APPEARS IN
संबंधित प्रश्न
If f(x) = (x − a)2 (x − b)2, find f(a + b).
If \[f\left( x \right) = \begin{cases}x^2 , & \text{ when } x < 0 \\ x, & \text{ when } 0 \leq x < 1 \\ \frac{1}{x}, & \text{ when } x \geq 1\end{cases}\]
find: (a) f(1/2), (b) f(−2), (c) f(1), (d)
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
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:
(i) 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:
(vi) \[2f - \sqrt{5} g\]
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
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) = ex−[x], x ∈ R.
If f(x) = 4x − x2, x ∈ R, then write the value of f(a + 1) −f(a − 1).
If f(x) = cos (log x), then the value of f(x2) f(y2) −
If \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) =
The domain of definition of the function f(x) = log |x| is
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(3)
Which of the following relations are functions? 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)}
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Write the following expression as sum or difference of logarithm
`log (sqrt(x) root(3)(y))`
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
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:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
Answer the following:
If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Answer the following:
Find the range of the following function.
f(x) = |x – 5|
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(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
The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
Find the domain of the following function.
f(x) = [x] + x
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
The range of the function y = `1/(2 - sin3x)` is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
Range of the function f(x) = `x/(1 + x^2)` is ______.
