मराठी

Every Invertible Function is - Mathematics

Advertisements
Advertisements

प्रश्न

Every invertible function is

पर्याय

  • monotonic function

  • constant function

  • identity function

  • not necessarily monotonic function

MCQ

उत्तर

monotonic function
We know that "every invertible function is a monotonic function".

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Increasing and Decreasing Functions - Exercise 17.4 [पृष्ठ ४१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 17 Increasing and Decreasing Functions
Exercise 17.4 | Q 19 | पृष्ठ ४१

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is

(a) strictly increasing

(b) strictly decreasing


Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.


Find the value of c in Rolle's theorem for the function `f(x) = x^3 - 3x " in " (-sqrt3, 0)`


Show that the function given by f(x) = 3x + 17 is strictly increasing on R.


Find the intervals in which the following functions are strictly increasing or decreasing:

 (x + 1)3 (x − 3)3


Prove that the function f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`


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) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.


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) = 8 + 36x + 3x2 − 2x?


Find the interval in which the following function are increasing or decreasing f(x) = −2x3 − 9x2 − 12x + 1  ?


Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)?


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 an increasing function on (−π/2, π/2) ?


Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?


Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?


Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?


Write the set of values of k for which f(x) = kx − sin x is increasing on R ?


The interval of increase of the function f(x) = x − ex + tan (2π/7) is


In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is


Function f(x) = | x | − | x − 1 | is monotonically increasing when

 

 

 

 

 

 

 

 

 

 

 


The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.


Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π).


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. 


Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.


Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.


Solve the following:

Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.


Test whether the following function is increasing or decreasing.

f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0


Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function


If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______


In which interval is the given function, f(x) = 2x3 - 21x2 + 72x + 19 monotonically decreasing?


Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R


The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.


The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is


Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.


Function f(x) = x100 + sinx – 1 is increasing for all x ∈ ______.


Let f(x) = `x/sqrt(a^2 + x^2) - (d - x)/sqrt(b^2 + (d - x)^2), x ∈ R` where a, b and d are non-zero real constants. Then ______.


Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×