Home
Class 12
MATHS
Which of the following statement is alwa...

Which of the following statement is always true? (a)If `f(x)` is increasing, then `f^(-1)(x)` is decreasing. (b)If `f(x)` is increasing, then `1/(f(x))` is also increasing. (c)If `fa n dg` are positive functions and `f` is increasing and `g` is decreasing, then `f/g` is a decreasing function. (d)If `fa n dg` are positive functions and `f` is decreasing and `g` is increasing, the `f/g` is a decreasing function.

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that f(x)=x-sinx is an increasing function.

The function f(x) = x^(2) is decreasing in

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

Which of the following statements is always true? ([.] represents the greatest integer function. a) If f(x) is discontinuous then |f(x)| is discontinuous b) If f(x) is discontinuous then f(|x|) is discontinuous c) f(x)=[g(x)] is discontinous when g(x) is an integer d) none of these

If fogoh(x) is an increasing function, then which of the following is possible? (a) f(x),g(x),a n dh(x) are increasing (b) f(x)a n d h(x) are increasing and g(x) is decreasing (c) f(x),g(x),a n dh(x) are decreasing

Find the intervals of increasing and decreasing function for f(x)=x^(3)+2x^(2)-1 .

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,pi/e), decreasing in (pi/e ,oo) decreasing in (0,pi/e), increasing in (pi/e ,oo)

Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then h is increasing whenever f is increasing h is increasing whenever f is decreasing h is decreasing whenever f is decreasing nothing can be said in general

Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Statement 2: If both f(x)a n dg(x) are increasing in (a , b),t h e nf(x)g(x) must be increasing in (a,b).

If f(x)=xe^(x(x−1)) , then f(x) is (a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]