Mathematics

Inverses in Mathematics

90 Questions

Inverses in mathematics cover additive, multiplicative, and matrix operations. These concepts test the ability to reverse mathematical functions and transformations. Such questions frequently appear in various competitive examinations to evaluate fundamental algebraic skills.

Additive inverseMultiplicative inverseMatrix inversionInverse functionsLinear transformations

Inverses in Mathematics Questions

Multiple choice maths matrix properties of matrix multiplication properties of multiplication of matrix multiplication of matrices

Consider two matrix $A = \begin{bmatrix} 1 & 2\ 2 & 1\ 1 & 1 \end{bmatrix}$ and $ B = \begin{bmatrix} 1 & 2 & -4\  2 & 1 & -4 \end{bmatrix}$. Which one of the following is correct ?

  1. B is the right inverse of A

  2. B is the left inverse of A

  3. B is the both sided inverse of A

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For two $m \times  n$ and $n \times m$ matrices $A$ and $B$

If $AB =I$, then $B$ is right inverse of $A$
If $BA=I$, then $B$ is left inverse of $A$
Note that if $AB=BA=I$, $B$ is both sided inverse of $A$
If $m=n$, which isn't true here
$AB=\begin{bmatrix} 1 & 2 \ 2 & 1 \ 1 & 1 \end{bmatrix}\begin{bmatrix} 1 & 2 & -4 \ 2 & 1 & -4 \end{bmatrix}=\begin{bmatrix} 5 & 4 & -4 \ 4 & 5 & -4 \ 3 & 3 & 0 \end{bmatrix}\neq I$
$BA=\begin{bmatrix} 1 & 2 & -4 \ 2 & 1 & -4 \end{bmatrix}\begin{bmatrix} 1 & 2 \ 2 & 1 \ 1 & 1 \end{bmatrix}=\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}=I$
$\therefore$ B is left inverse of A

Multiple choice

The additive inverse of a negative integer

  1. is always negative

  2. is always positive

  3. is the same integer

  4. Zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The additive inverse of a number x is -x. If x is negative, -x is positive (e.g., the inverse of -5 is 5).

Multiple choice

Additive inverse of -a is

  1. a

  2. 1/a

  3. -a

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The additive inverse of a number x is -x. Therefore, the additive inverse of -a is -(-a), which equals a.

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

The additive inverse of $\sqrt { 3 } -2\quad is$_____________

  1. $\sqrt { 3 } +2$
  2. $-\sqrt { 3 } +2$
  3. $-\sqrt { 3 } -2$
  4. $\sqrt { 3 } +\sqrt { 2 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The additive inverse of a number a is the number that, when added to a, yields zero. 
This number is also known as the opposite (number), sign change, and negation.

$Additive \ Inverse \ of (\sqrt {3}-2 )\ is$
$\rightarrow -(\sqrt{3}-2)$
$\rightarrow -\sqrt{3}+2$
$\rightarrow B \ is \ correct \ answer$
Multiple choice

What is the inverse of the function (f(x) = 2x + 1)?

  1. \(f^{-1}(x) = \frac{x - 1}{2}\)
  2. \(f^{-1}(x) = \frac{x + 1}{2}\)
  3. \(f^{-1}(x) = 2x - 1\)
  4. \(f^{-1}(x) = -2x + 1\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The inverse of a function (f(x)) is the function (f^{-1}(x)) such that (f(f^{-1}(x)) = x) and (f^{-1}(f(x)) = x). To find the inverse of (f(x) = 2x + 1), we can solve for (x) in terms of (f(x)): (f(x) = 2x + 1) (\Rightarrow 2x = f(x) - 1) (\Rightarrow x = \frac{f(x) - 1}{2}) (\therefore f^{-1}(x) = \frac{x - 1}{2}).

Multiple choice

What is the inverse of the function (f(x) = 3x - 2)?

  1. \(f^{-1}(x) = \frac{x + 2}{3}\)
  2. \(f^{-1}(x) = \frac{x - 2}{3}\)
  3. \(f^{-1}(x) = \frac{1}{3}x + 2\)
  4. \(f^{-1}(x) = \frac{1}{3}x - 2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The inverse of a function is the function that undoes the original function.

Multiple choice

What is the additive inverse of an element in a field?

  1. The element itself

  2. The opposite of the element

  3. The reciprocal of the element

  4. The square root of the element
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The additive inverse of an element in a field is the element that, when added to the original element, results in the additive identity. In the set of real numbers, the additive inverse of an element is its opposite.

Multiple choice

What is the additive inverse of a number?

  1. The number itself

  2. The opposite of the number

  3. The reciprocal of the number

  4. The square root of the number
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The additive inverse of a number is the number that, when added to the original number, results in zero. This is also known as the opposite of the number.

Multiple choice

What is the multiplicative inverse of a number?

  1. The number itself

  2. The opposite of the number

  3. The reciprocal of the number

  4. The square root of the number
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The multiplicative inverse of a number is the number that, when multiplied by the original number, results in one. This is also known as the reciprocal of the number.

Multiple choice

What is the inverse of a function?

  1. A function that undoes the original function

  2. A function that is the opposite of the original function

  3. A function that has the same domain and codomain as the original function

  4. A function that has the same range as the original function
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The inverse of a function is a function that undoes the original function, meaning that if you apply the inverse function to the output of the original function, you get the input.

Multiple choice

What is the inverse of a function?

  1. A function that undoes the original function

  2. A function that has the same domain and codomain as the original function

  3. A function that has the same graph as the original function

  4. A function that has the same equation as the original function
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The inverse of a function is a function that undoes the original function, meaning that if you apply the inverse function to the output of the original function, you get the input.

Multiple choice

What is the inverse of the relation {(1, 2), (2, 3), (3, 1)}?

  1. {(2, 1), (3, 2), (1, 3)}

  2. {(1, 3), (2, 1), (3, 2)}

  3. {(3, 1), (1, 2), (2, 3)}

  4. {(3, 2), (1, 3), (2, 1)}
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The inverse of a relation is the relation that consists of all the ordered pairs (b, a) such that (a, b) is in the original relation. In this case, the inverse of the relation {(1, 2), (2, 3), (3, 1)} is {(2, 1), (3, 2), (1, 3)}.

Multiple choice

What is the additive inverse of an element in a ring?

  1. The element that, when added to the given element, results in the zero element.

  2. The element that, when multiplied by the given element, results in the zero element.

  3. The element that, when added to itself, results in the given element.

  4. The element that, when multiplied by itself, results in the given element.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The additive inverse of an element a in a ring is the element -a such that a + (-a) = 0, where 0 is the zero element of the ring. The other options are not correct because they do not accurately define the additive inverse of an element in a ring.