Which of the following pairs of functions are inverses of each other? A. F(x)-6(4/x)-12 and g(x)-x/24 +12
B. f(x)=5(x/4) -3 and g(x) -4(x+3)/5
C. f(x) = x-2/7+8 and g(x) = 7(x + 2) - 8
D. f(x) = 6(x - 2)+3 and g(x) - x+2/6 -3

The correct pairs of functions that are inverses of each other is [f(x)=5(x/4) -3] and [g(x) = 4(x+3)/5] and this can be determined by replacing f(x) by x and x by g(x) in the function f(x).

Check all the options in order to determine the correct pairs of functions that are inverses of each other.

A)

First, replace f(x) by x and x by g(x) in the function f(x).

Now, solve the above expression for g(x).

So, this option is incorrect.

B)

First, replace f(x) by x and x by g(x) in the function f(x).

Now, solve the above expression for g(x).

So, this option is correct. Therefore, no need to check the remaining options.

For more information, refer to the link given below:

link

B. f(x) = 5(x/4) - 3 and g(x) = [4(x + 3)]/5

Step-by-step explanation:

In the figure attached, the question is shown (the order of the options are different).

To find the inverse of a function, first, replace x with g(x) and f(x) with x, as follows:

f(x) = 5(x/4) - 3

x = 5(g(x)/4) - 3

Next, isolate g(x), as follows:

x + 3 = 5(g(x)/4)

4(x + 3) = 5g(x)

[4(x + 3)]/5 = g(x)

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign