## Inverse Questions and Answers in Aptitude

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.’

A function ‘f’ includes an inverse function only when every ‘y’ is available in its range. There is the only available value of ‘x’ in its domain for which ‘f(x)=y: The function of inverse is unique and is symbolized as $f^{-1}$ and is known as “f inverse.”

### 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.

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

-1

-1

2

2

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))

$8x^{2}$

$8x^{2}$

$5x^{2}$

$5x^{2}$

$7x^{2}$

$7x^{2}$

$2x^{2}$

$2x^{2}$

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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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