Is every invertible function monotonic?

Prove that every rational function is continuous.

Let f be a real-valued invertible function such that f((2x-3)/(x-2))=5x-2, x!=2. Then value of f^(-1)(13) is________

f(x)=[x] is step-up function. Is it a monotonically increasing function for x in R ?

Let f:A->A be an invertible function where A= {1,2,3,4,5,6} The number of these functions in which at least three elements have self image is

Consider the function h(x)=(g^(2)(x))/(2)+3x^(3)-5 , where g(x) is a continuous and differentiable function. It is given that h(x) is a monotonically increasing function and g(0) = 4. Then which of the following is not true ?

Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x+b has exactly one extremum. Statement 2: If a cubic function is monotonic, then its graph cuts the x-axis only one.

If f(x) is monotonic differentiable function on [a , b] , then int_a^bf(x)dx+int_(f(a))^(f(b))f^(-1)(x)dx= (a) bf(a)-af(b) (b) bf(b)-af(a) (c) f(a)+f(b) (d) cannot be found

Given a real-valued function f which is monotonic and differentiable. Then int_(f(a))^(f(b))2x(b-f^(-1)(x))dx=

It A is an invertible matrix, then which of the following is not true.

Let f be continuous and differentiable function such that f(x) and f'(x) has opposite signs everywhere. Then (A) f is increasing (B) f is decreasing (C) |f| is non-monotonic (D) |f| is decreasing