The function [tex]\rm f(g(x)) = \sqrt{2x}[/tex] and the function [tex]\rm g(f(x)) =2\sqrt{x}[/tex] and the function f(x) is not the inverse of g(x) and this can be determined by using the given data.
Given :
- [tex]\rm f(x) = \sqrt{x}[/tex]
The following steps can be used in order to determine the f(g(x)) and g(f(x)):
Step 1 - First write the given functions.
[tex]\rm f(x) = \sqrt{x}[/tex]
[tex]\rm g(x) = 2x[/tex]
Step 2 - Now, the function f(g(x)) is given by replacing x with g(x) in the function f(x).
[tex]\rm f(g(x)) = \sqrt{g(x)}[/tex]
Step 3 - Substitute the value of g(x) in the above expression.
[tex]\rm f(g(x)) = \sqrt{2x}[/tex]
Step 4 - Now, the function g(f(x)) is given by replacing x with f(x) in the function g(x).
[tex]\rm g(f(x)) =2f(x)[/tex]
Step 5 - Substitute the value of f(x) in the above expression.
[tex]\rm g(f(x)) =2\sqrt{x}[/tex]
Step 6 - The inverse of f(x) can be determined by replacing x by f(x) and f(x) by x.
[tex]\rm \sqrt{f(x)} = x[/tex]
[tex]\rm x^2 = f(x)[/tex]
Step 7 - Now, the inverse of g(x) is given by:
[tex]\rm 2g(x) = x[/tex]
[tex]\rm g(x) = \dfrac{x}{2}[/tex]
The function [tex]\rm f(g(x)) = \sqrt{2x}[/tex] and the function [tex]\rm g(f(x)) =2\sqrt{x}[/tex] and the function f(x) is not the inverse of g(x).
For more information, refer to the link given below:
https://brainly.com/question/12431044
