Respuesta :
Answer:
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)
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)
[tex]f(x) = 6\times \dfrac{4}{x}-12[/tex]
[tex]g(x) = \dfrac{x}{24}+12[/tex]
First, replace f(x) by x and x by g(x) in the function f(x).
[tex]x = 6\times \dfrac{4}{g(x)}-12[/tex]
Now, solve the above expression for g(x).
[tex]\dfrac{24}{g(x)} = x+12[/tex]
[tex]g(x) = \dfrac{x+12}{24}[/tex]
So, this option is incorrect.
B)
[tex]f(x) = 5\times \dfrac{x}{4}-3[/tex]
[tex]g(x) = \dfrac{4(x+3)}{5}[/tex]
First, replace f(x) by x and x by g(x) in the function f(x).
[tex]x = 5\times \dfrac{g(x)}{4}-3[/tex]
Now, solve the above expression for g(x).
[tex]\dfrac{4(x+3)}{5}=g(x)[/tex]
So, this option is correct. Therefore, no need to check the remaining options.
For more information, refer to the link given below:
https://brainly.com/question/15395662
