The inverse of the given function is [tex]\rm f^{-1}(x) = \dfrac{4x - 5 }{2}[/tex] and this can be determined by replacing x by f(x) and f(x) by x and then solving for f(x) and then replacing f(x) by [tex]\rm f^{-1}(x)[/tex].
Given :
[tex]\rm f(x) = \dfrac{2x+5}{4}[/tex]
The following steps can be used in order to determine the inverse of the given function:
Step 1 - Write the given function.
[tex]\rm f(x) = \dfrac{2x+5}{4}[/tex]
Step 2 - Now, to determine the inverse of the given function, replace x by f(x) and f(x) by x and then solve for f(x) and then replace f(x) by [tex]\rm f^{-1}(x)[/tex].
[tex]\rm x = \dfrac{2f(x)+5}{4}[/tex]
Step 3 - SImplify the above expression in order to determine the value of f(x).
4x = 2f(x) + 5
[tex]\rm f(x) = \dfrac{4x - 5 }{2}[/tex]
Step 4 - Replace f(x) by [tex]\rm f^{-1}(x)[/tex] in the above expression.
[tex]\rm f^{-1}(x) = \dfrac{4x - 5 }{2}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/5245372
