Identity Function

Q.

What are the properties of a matrix?

Q. If {(a, 8), (6, b)} represents an identity function, then the value of a and b are respectively ?

1. 6, 8
2. 6, 6
3. 8, 8
4. 8, 6

Q.

How many of the following statements are true about the identity function. Mention the correct number of statement(s).

(a) It's graph is shown above.
(b) Domain is R
(c) Range is R
(d) Its an even function

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Q. If {(2, a), (b, 8)} is an identity function, then the value of (a, b) is

1. (2, 8)
2. (8, 2)
3. (1, 4)
4. (4, 1)

Q. If a robot is moving from origin (base) as per the following log:


The final x- and y-coordinates of the robot are .

1. x = 1/3, y = 1/2
2. x = 1/8, y = 1/3
3. x = 1/3, y = 1/8
4. x = 1/8, y = 5/2

Q. If {(x, -1), (2y, 6), (1, -z)} is an identity function, what is the value of x + y + z?

1. 1

Q. Prove the following identity:
$f^{\prime }\left(x\right)+f\left(x\right)+f\left(\frac{1}{x}\right)-\frac{1}{x}=0$ if $f\left(x\right)=\ln x$