Home
Class 12
MATHS
Consider alpha gt 1 and f:[1/alpha,alpha...

Consider `alpha gt 1` and `f:[1/alpha,alpha] rarr [1/alpha,alpha]` be bijective function. Suppose that `f^(-1)(x)=1/f(x), " for all " in [1/alpha,alpha]`.
Which of the following statements can be concluded about (f(x))?

A

f(x) is discontinuous in `[1/alpha, alpha]`

B

f(x) is increasing in `[1/alpha, alpha]`

C

f(x) is decreasing in `[1/alpha, alpha]`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
b
Promotional Banner

Similar Questions

Explore conceptually related problems

Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bijective function. Suppose that f^(-1)(x)=1/f(x), " for all " in [1/alpha,alpha] . Which of the following statements can be concluded about f(f(x))?

Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bijective function. Suppose that f^(-1)(x)=1/f(x), " for all " x in [1/alpha,alpha] . Then f(1) is equal to

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

The value of parameter alpha , for which the function f(x) = 1+alpha x, alpha!=0 is the inverse of itself

F(x)=x^(5)+log,(x+sqrt(1+x^(2))) , Then for all alpha, beta in R such that alpha+beta gt 0

Let f(x)=(alphax)/(x+1),x ne -1 . Then, for what values of alpha is f[f(x)]=x?

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

if [ ( cos alpha, - sin alpha),(sin alpha, cos alpha)] and A +A^1 =I then alpha =……

Find P and alpha by converting equation x+y =1 in xcos alpha + y sin alpha = P form.

Integrate the functions 1/(sqrt(sin^(3)xsin(x+alpha))