Advertisements
Advertisements
प्रश्न
Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3
उत्तर
We know that
when x > 0
|x – 2| is (x – 2), x ≥ 2
|2 + x| is (2 + x), x ≥ –2
when x > 0
|x – 2| is –(x – 2), x < 2
|2 + x| is –(2 + x), x <–2
Given that, f(x) = |x – 2| + |2 + x|, –3 ≤ x ≤ 3
It can be rewritten as,
f(x) = `{{:(-(x - 2) - (2 + x)",", -3 ≤ x < - 2),(-(x - 2) + (2 + x)",", -2 ≤ x < 2),((x - 2) + (2 + x)",", 2 ≤ x ≤ 3):}`
Or
f(x) = `{{:(-x + 2 - 2 - x",", -3 ≤ x < -2),(-x + 2 + 2 + x",", -2 ≤ x < 2),(x - 2 + 2 + x",", 2 ≤ x ≤ 3):}`
Or
f(x) = `{{:(-2x",", -3 ≤ x < -2),(4",", -2 ≤ x < 2),(2x",", 2 ≤ x ≤ 3):}`
APPEARS IN
संबंधित प्रश्न
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(b) f2 = {(1, 1), (2, 7), (3, 5)}
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
Write the domain and range of \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
Check if the following relation is function:
Which of the following relations are functions? If it is a function determine its domain and range:
{(1, 1), (3, 1), (5, 2)}
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
Find the domain and range of the following function.
f(x) = `sqrt((x - 2)(5 - x)`
Find the domain and range of the following function.
f(x) = `sqrt(16 - x^2)`
Express the area A of circle as a function of its circumference C.
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x3
lf f(x) = 3(4x+1), find f(– 3)
Express the following exponential equation in logarithmic form
`9^(3/2)` = 27
If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b
If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
Answer the following:
If b2 = ac. prove that, log a + log c = 2 log b
Answer the following:
Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3
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(2a)
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to ______.
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)
