Advertisements
Advertisements
प्रश्न
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
उत्तर
f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
= `{(-x + 1 - 1 - x",", -2 ≤ x < -1),(-x + 1 + x + 1",", -1 ≤ x < 1),(x - 1 + 1 + x",", 1 ≤ x ≤ 2):}`
= `{{:(-2x",", -2 ≤ x < - 1),(2",", -1 ≤ x < 1),(2x",", 1 ≤ x ≤ 2):}`
APPEARS IN
संबंधित प्रश्न
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
Write the range of the function f(x) = ex−[x], x ∈ R.
Which of the following are functions?
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
If ƒ(m) = m2 − 3m + 1, find f(x + 1)
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(3)
If f(x) = 3x + a and f(1) = 7 find a and f(4).
Check if the following relation is a function.
Check if the relation given by the equation represents y as function of x:
x2 − y = 25
If f(m) = m2 − 3m + 1, find f(x + 1)
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((x - 3)/(7 - x))`
Express the area A of circle as a function of its diameter d
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Express the following logarithmic equation in exponential form
log2 64 = 6
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Prove that `"b"^(log_"b""a"` = a
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)`
A function f is defined by f(x) = 2x – 3 find x such that f(x) = x
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
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
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)
The function f: R `rightarrow` R defined by f(x) = sin x is ______.
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.
If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.
The period of the function
f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.
