Question

Which of the following pairs of functions are inverses of each other ​

Answer 1

Option (A) represents the function and its inverse of a function option (A) is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function and inverse of a function shown in the picture.

Checking for option (A):

$\rm f(x) = \dfrac{x}{4}+10 \ \ \ and \ \ \ g(x) = 4x -10$

Taking f(x):

$\rm f(x) = \dfrac{x}{4}+10$

To find the inverse of a function interchange the x and y variables:

f(x) → x

x  → g(x)

$\rm x = \dfrac{g(x)}{4}+10$

Solving:

4x = g(x) + 10

g(x) = 4x - 10

Similarly, we can find the inverse of a function.

Thus, option (A) represents the function and its inverse of a function option (A) is correct.

Learn more about the function here:

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Answer 2

The answer is C.

$f(x) =\frac{12}{x} -18 \\g(x) = \frac{12}{x-8}$

Step by step ex[planation:

To solve for the inverse of the first function

Replace f(x) or g(x) with y, switch x and y, solve for y and replace it with f⁻¹(x)

Here , the option C is correct because:

f(x)=18/x-9

y=18/x-9

x=18/y-9

x+9=18/y

y(x+9)=18

y=18/(x+9)

f⁻¹(x)=18/(x+9)

So , the correct, the answer is C