# Inverse Questions ## Definition of Inverse

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

• 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 4x/5

4x/5

x/20

x/20

x-20/4

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) = ½ 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) = 1/y

f-1 = (y) = x, if and only if f(x) = 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) = 2/y

f-1 = (y) = x, if and only if f(x) = 2/y

None of the above

None of the above

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Question 5 Time: 00:00:00
Find the inverse of the matrix A = 5       8 7       2 . 2 8 7 5

2 8 7 5

5 8 7 2

5 8 7 2

5 8 2 7

5 8 2 7

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 = 16 -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 (y-3)/6

(y-3)/6

Y-3

Y-3

(y-3)/2

(y-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) = 1+4x 2+x 4x-3/ 2-9x

4x-3/ 2-9x

2x-1/ 4-x

2x-1/ 4-x

x+6

x+6

none

none

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Question 9 Time: 00:00:00

1. 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= 1/y. 1/y

1/y

1/x

1/x

1/2x

1/2x

None

None

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