Identity Function

Q.

Let $M$ be a $3\times 3$ invertible matrix with real entries.Let $M$ be a $3\times 3$ invertible matrix with real entries and let $I$denote the $3\times 3$ identity matrix. If $M^{-1}=adj(adjM),$then which of the following statements is/are always true?

1. $M=I$

2. $detM=1$

3. $M^2=I$

4. ${(adjM)}^2=I$

Q. Which of the following is true for identity function?

1. It is a straight line parallel to $x-$ axis
2. It is a straight line parallel to $y-$ axis
3. It is a straight line passing through origin
4. It is not a straight line

Q. A function is defined from $A$ to $B,$ where number of elements in $A$ and $B$ are $2$ and $6$ respectively. If the total number of functions is $x$ and total number of one one functions is $y,$ then the value of $x+y$ is

Q. For the two functions given as $f\left(x\right)=\ln (x-8)+7,g\left(x\right)=\ln x$,
which of the following denotes the transformations of the function $g\left(x\right)$ to obtain the function $f\left(x\right)$

1. Translate $8$ units to the right and $7$ units down
2. Translate $8$ units to the left and $7$ units up
3. Translate $7$ units to the left and $8$ units down
4. Translate $8$ units to the right and $7$ units up

Q. The domain and range is always equal for

1. Identity function
2. Constant function
3. None of these
4. Signum function

Q.

The number of values of the pair (a, b) for which $a(x+1{)}^2+b(x^2-3x-2)+x+1=0$ is an identity in x is

1. 1

2. 2

3. infinite

4. 0

Q.

Expand ${\left(2x-\frac{2}{x}\right)}^3$.

Q. Which of the following functions are identity functions?

1. $f:R\to R,f\left(x\right)=x$
2. $g:N\to Z,g\left(p\right)=3$
3. $h:z\to z,h\left(y\right)=y$
4. $g:N\to N,g\left(z\right)=z$

Q. State whether the following statement is True or False.
The inverse of an identity function is the identity function itself.

1. True
2. False

Q. Which of the following represents identity function?

1. $f:R\to R,f\left(x\right)=-x$
2. $f:R\to R,f\left(x\right)=2x$
3. $f:R\to R,f\left(x\right)=x$
4. $f:Z\to Z,f\left(x\right)=x$

Q. If $\left\{\right(x,2),(4,y\left)\right\}$ represents an identity function, then $(x,y)$ is :

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

Q. The domain and range is always equal for

1. Constant function
2. Identity function
3. Signum function
4. None of these

Q. If f is even function and g is an odd function, then $f_{o}g$ is ............function.

1. Even
2. Odd
3. Either even
4. Neither even nor odd

Q. Find if the given below operation has identity?

(v) $a\ast b=\frac{ab}{4}$

Q. Let $f$ be an injective map with domain {x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false :
$f\left(x\right)=1,f\left(y\right)\sqrt{1},f\left(z\right)\sqrt{2}$. The value of $f^{-1}\left(1\right)$ is

1. x
2. z
3. none of these
4. y

Q.

Which of the following is the identity function?

1. $y=|x|$

2. $y=x$

3. $y=x^2$

4. $y=1$

Q. Show that, if $f:R-\left\{\frac{7}{5}\right\}\to R-\left\{\frac{3}{5}\right\}$ is defined by f (x) = $\frac{3x+4}{5x-7}$ and $g:R-\left\{\frac{3}{5}\right\}\to R-\left\{\frac{7}{5}\right\}$ is defined by g(x) = $\frac{7x+4}{5x-3}$,
then log = $l_A$ and gof = $l_B$, where $l_A$ and $l_B$ are called identity functions on sets A and B.

Q. $f:B\to B$, if $f\left(x\right)=x$, then the function $f$ is

Q. The graph of an Identity function is?

1. A straight line parallel to Y axis
2. A straight line parallel to X axis
3. A straight line passing through the origin
4. None

Q. The number of elements of an identity function defined on a set containing four elements is______

1. $2^2$
2. $2^4$
3. $2^{16}$
4. $2^8$

Q.

Find the value of $y$, if :

$3y={\left(25\right)}^2-{\left(13\right)}^2$

Q. If $f\left(x\right)=\frac{2x+3}{3x-2}$
Prove that $fof$ is an identity function

Q.

Which of the following is the identity function?

1. $y=1$

2. $y=x^2$

3. $y=|x|$

4. $y=x$

Q.

Expand ${\left(\frac{4}{5}x-2\right)}^3$.

Q. Which of the following is true for identity function?

1. It is a straight line parallel to $x-$ axis
2. It is a straight line parallel to $y-$ axis
3. It is a straight line passing through origin
4. It is not a straight line

Q.

How many of the following statements are true about the identity function?

(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.

How many of the following statements are true about the identity function?

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

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