Inverse Questions and Answers

August 2, 2023

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.’

Inverse Questions and Answers

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.

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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

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

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

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

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

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

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

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

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

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

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}

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

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)  

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

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

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

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

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

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

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}

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

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

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

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

Question 25

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

126

126

127

127

128

128

122

122

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}

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

Question 28

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

39

39

29

29

42

42

45

45

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

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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