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.

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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)

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

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