## Inverse Questions and Answers in Aptitude

On this page you will gwt to know about the Inverse question and Answers.The Inverse is known as a function, which opens the act of some other function. ‘g’ is called the inverse of function f if where ever ‘y = f(x)’ then, ‘x = g(y): It can also be written in the term of the arrangement of  ‘f ‘ and ‘g’ as ‘g(f(x)) = x.’

### Rules of Inverse

• Inverse functions are one to one functions.
• If the function f(x) = $x^2$, then it does not have an inverse function. It can be easily understood with the example, $f^{-1}$ (4) could be written as $f^{-1}$ (4) = 2, or it could also be written as $f^{-1}$ (4) = -2
• If the domain of ‘f’ is restricted to the negative or positive real number only, then its function will have an inverse.

### Inverse Rational Function :

A rational function is a function of form f(x) = P(x)/Q(x) where Q(x) ≠ 0. To find the inverse of a rational function, follow the following steps.

Step 1: Replace f(x) = y
Step 2: Interchange x and y
Step 3: Solve for y in terms of x
Step 4: Replace y with f-1(x) and the inverse of the function is obtained.

## Also Check Out

Question 1

Time: 00:00:00
Find the inverse of the function f(x) = 4x +20

$\frac{4x}{5}$

$\frac{4x}{5}$

$\frac{x}{20}$

$\frac{x}{20}$

$y= \frac{x-20}{4}$

$y= \frac{x-20}{4}$

Not Determined

Not Determined

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Question 2

Time: 00:00:00
If f(x) = x + 12. Calculate the value of $f^{-1} (x)$.

x-12

x-12

1

1

x-11

x-11

x

x

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Question 3

Time: 00:00:00
If $g(x) = \frac{1}{2}x+ 4$, find the value of $g^{-1}(x)$

x + 13

x + 13

2x -8

2x -8

x -2

x -2

None

None

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Question 4

Time: 00:00:00
Which of the following equation is true for inverse functions?

$f^{-1}$= (y) = x, if and only if f(x) = $\frac{1}{y}$

$f^{-1}$= (y) = x, if and only if f(x) = $\frac{1}{y}$

$f^{-1}$= (y) = x, if and only if f(x) = y

$f^{-1}$= (y) = x, if and only if f(x) = y

$f^{-1}$ = (y) = x, if and only if f(x) = $\frac{2}{y}$

$f^{-1}$ = (y) = x, if and only if f(x) = $\frac{2}{y}$

None of the above

None of the above

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Question 5

Time: 00:00:00
Inverse of 32x +5 will be

$\frac{x-5}{32}$

$\frac{x-5}{32}$

$y = \frac{x-4}{32}$

$y = \frac{x-4}{32}$

$y = \frac{x-3}{32}$

$y = \frac{x-3}{32}$

Cannot be determined

Cannot be determined

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Question 6

Time: 00:00:00
What will be the value of the inverse function (x + 3)4 - 8 = y

(x-4)/4

(x-4)/4

(x-4)/5

(x-4)/5

10

10

Not Determined

Not Determined

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Question 7

Time: 00:00:00
Find the inverse of f(x) = 3x + 5

$\frac{x-1}{2}$

$\frac{x-1}{2}$

$\frac{x-4}{2}$

$\frac{x-4}{2}$

$\frac{x-3}{2}$

$\frac{x-3}{2}$

None of the above

None of the above

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Question 8

Time: 00:00:00
Calculate the inverse of the function f(x) = 27 - 4x

$\frac{27-2x}{4}$

$\frac{27-2x}{4}$

$\frac{27-x}{4}$

$\frac{27-x}{4}$

$\frac{27-x}{2}$

$\frac{27-x}{2}$

none

none

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Question 9

Time: 00:00:00
Let the inverse function of f be g and let us assume we know the following values of f

f(-1) = 0

f (0) =1

f(1) =2

Find the values of g (0) and g (1)

-1, 0

-1, 0

1, 1

1, 1

0, 0

0, 0

None of the above

None of the above

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Question 10

Time: 00:00:00
Calculate the value of the inverse function of $x = \frac{1}{y}$.

$\frac{1}{y}$

$\frac{1}{y}$

$\frac{1}{x}$

$\frac{1}{x}$

$\frac{1}{2x}$

$\frac{1}{2x}$

None

None

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Question 11

Time: 00:00:00
Find the inverse of the Function f(x) = 3x +9

$\frac{x-7}{3}$

$\frac{x-7}{3}$

$\frac{x-9}{3}$

$\frac{x-9}{3}$

$\frac{x-6}{3}$

$\frac{x-6}{3}$

$\frac{x-8}{3}$

$\frac{x-8}{3}$

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Question 12

Time: 00:00:00
If $f^{-1}(x) = 4x+5$ Find value of  $f^{-1}(5)$

24

24

25

25

23

23

21

21

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Question 13

Time: 00:00:00
What is the inverse function of $Sin(x)$?

$cos^{-1}(x)$

$cos^{-1}(x)$

$sin^{-1}(x)$

$sin^{-1}(x)$

$tan^{-1}(x)$

$tan^{-1}(x)$

$cosec^{-1}(x)$

$cosec^{-1}(x)$

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Question 14

Time: 00:00:00
What is the value of $Sin^{-1}(\frac{1}{2})$?

$30\degree$

$30\degree$

$90\degree$

$90\degree$

$60\degree$

$60\degree$

None

None

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Question 15

Time: 00:00:00
What is the inverse of Function y = 7x

$\frac{1}{7}\times x$

$\frac{1}{7}\times x$

$\frac{1}{7}\times y$

$\frac{1}{7}\times y$

7x

7x

None

None

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Question 16

Time: 00:00:00
f(x) = 2x and g(x) = 4x Find f(g(x))

8x

8x

5x

5x

7x

7x

2x

2x

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Question 17

Time: 00:00:00
What is the value of $tan^{-1}(1)$?

$45\degree$

$45\degree$

$90\degree$

$90\degree$

$135\degree$

$135\degree$

$0\degree$

$0\degree$

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Question 18

Time: 00:00:00
Find the value of f(2) if f(x) = 23x + 34

70

70

80

80

60

60

50

50

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Question 19

Time: 00:00:00
Inverse of a  Particular Function is $3x^{2} + 4x +7$ Find $f^{-1}(2)$

25

25

27

27

28

28

22

22

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Question 20

Time: 00:00:00
What will be the  inverse function of (2x + 3)3 - 6 = y

(x -3)/8

(x -3)/8

(x -3)/7

(x -3)/7

(x -3)/6

(x -3)/6

$\frac{-3}{2}$

$\frac{-3}{2}$

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Question 21

Time: 00:00:00
Let the inverse function of f be g and let us assume we know the following values of f(4) = 6 , f(7) = 9 , f(2) =4 Find g(9)

4

4

5

5

7

7

6

6

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Question 22

Time: 00:00:00
Value of $tan^{-1}(\frac{1}{x})$ will be

$cot^{-1}(x)$

$cot^{-1}(x)$

$sec^{-1}(x)$

$sec^{-1}(x)$

$cosec^{-1}(x)$

$cosec^{-1}(x)$

None

None

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Question 23

Time: 00:00:00
Value of $cos^{-1}(cos\theta)$ where $\theta$ belongs to $[\frac{-\pi}{2} ,\frac{\pi}{2}]$

$2\theta$

$2\theta$

$\theta$

$\theta$

$3\theta$

$3\theta$

1

1

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Question 24

Time: 00:00:00
Let the inverse function of f be g and let us assume we know the following values of f(1) = 1 , f(2) = 4 , f(3) =9 Find g (4)

3

3

5

5

2

2

1

1

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Question 25

Time: 00:00:00
Find Value of f(4) in $f(x) = 33x - 6$

126

126

127

127

128

128

122

122

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Question 26

Time: 00:00:00
Find Inverse of This Function $f(x) = \frac{2x+3}{3}$

$\frac{3x-3}{2}$

$\frac{3x-3}{2}$

$\frac{3x-3}{3}$

$\frac{3x-3}{3}$

$\frac{3x-3}{4}$

$\frac{3x-3}{4}$

$\frac{3x-2}{2}$

$\frac{3x-2}{2}$

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Question 27

Time: 00:00:00
Find the Principal Value of $cos^{-1}(1)$

$90\degree$

$90\degree$

$45\degree$

$45\degree$

$30\degree$

$30\degree$

$0\degree$

$0\degree$

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Question 28

Time: 00:00:00
Find f(3) $f(x) = 4x^{2} + 3x$

39

39

29

29

42

42

45

45

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Question 29

Time: 00:00:00
What will be the inverse function of (4x + 3)7 - 28 = y

(x + 7) / 35

(x + 7) / 35

(x + 7) / 20

(x + 7) / 20

(x + 7) / 28

(x + 7) / 28

(x + 6) / 20

(x + 6) / 20

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Question 30

Time: 00:00:00
If f(x) = 7x and g(x) = 2x Find f(g(x))

$18x^{2}$

$18x^{2}$

$15x^{2}$

$15x^{2}$

$12x^{2}$

$12x^{2}$

$14x^{2}$

$14x^{2}$

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