Advertisements
Advertisements
प्रश्न
Every invertible function is
पर्याय
monotonic function
constant function
identity function
not necessarily monotonic function
Advertisements
उत्तर
monotonic function
We know that "every invertible function is a monotonic function".
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
(x + 1)3 (x − 3)3
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 + 9x + 15 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = 3 x^4 - 4 x^3 - 12 x^2 + 5\] ?
Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?
Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
Find the intervals in which f(x) = (x + 2) e−x is increasing or decreasing ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Write the set of values of k for which f(x) = kx − sin x is increasing on R ?
State whether f(x) = tan x − x is increasing or decreasing its domain ?
The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval
Find the intervals in which the function \[f(x) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] is
(a) strictly increasing
(b) strictly decreasing
Find the intervals in which function f given by f(x) = 4x3 - 6x2 - 72x + 30 is (a) strictly increasing, (b) strictly decresing .
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.
The total cost of manufacturing x articles is C = 47x + 300x2 − x4. Find x, for which average cost is increasing.
Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing.
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
The function f(x) = x3 - 3x is ______.
The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______
If f(x) = x3 – 15x2 + 84x – 17, then ______.
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
Find the interval/s in which the function f : R `rightarrow` R defined by f(x) = xex, is increasing.
