Answer:
[tex](A)y=\frac{2.5}{x-4.1} + 2.8[/tex]
Step-by-step explanation:
In the expressions, the value at which the domain of the function will be the set of all real numbers except x=4.1 is the value at which 4.1 makes the denominator equal to zero, i.e makes the fraction undefined.
Given the options
[tex](A)y=\frac{2.5}{x-4.1} + 2.8[/tex]
Setting the denominator to zero, x-4.1=0, x=4.1. The fraction is undefined at x=4.1
[tex](B)y=\frac{2.8}{x+4.1} -2.5[/tex]
Setting the denominator to zero, x+4.1=0, x=-4.1. The fraction is undefined at x=-4.1
[tex](C)y=\frac{4.1}{x-2.8} +2.5[/tex]
Setting the denominator to zero, x-2.8=0, x=2.8. The fraction is undefined at x=2.8
[tex](D)y=\frac{4.1}{x-2.5} +2.8[/tex]
Setting the denominator to zero, x-2.5=0, x=2.5. The fraction is undefined at x=2.5
Therefore, function that has a domain of all real numbers except x=4.1 is:
[tex](A)y=\frac{2.5}{x-4.1} + 2.8[/tex]
