Properties of Inverse Function

Q. If $A=\left[\begin{array}{cc}4& -1\\ x& -3\end{array}\right]$ is an idempotent matrix, then the value of $x$ is

Q. p : xy = yx, is true for every real number x and y q : There exists real number x and y for which xy = yx. Above pair of statements are 1. negation of each other 2. not negation of each other 3. converse of each other 4. contrapositive of each other

Q.

If the relation R:A$\to$B where A={1, 2, 3, 4} and B={1, 3, 5} is defined by R={(x, y):x<y, x$\in$A, y$\in$B}, then $RO{R}^{-1}$ is

1. 

2. 

3. 

4. 

Q. 32. If the function f:(1, infinite)to(1, infinite) is defined byf(x)=2powerx(x-1), then f inverse x=

Q. Inverse of x+1/x+2

Q. 2tan inverse[(a-b)/(a+b)]^1/2tan(thita /2)

Q.

If a function f(x) is defined on [1, 4] $\to$ [1, 7] and given that f(3) = 5 and its inverse exists then find $f^{-1}$ ( f (5) ).

1. 3

2. 5

3. 7

4. Not defined

Q.

The inverse function of $f^{-1}\left(x\right),if{f}^{-1}\left(x\right)existsisf\left(x\right)$

1. True

2. False