The following values represent linear function ƒ(x) and rational function g(x).
ƒ(3) = 7 g(3) = 5.6
ƒ(4) = 5 g(4) = 6.7
a. determine whether or not there is a solution to the equation in 2-3 sentences describe whether there is a solution to the equation ƒ(x)=g(x) between x=3 and x=4. b. use complete sentences to justify your claim.

To affirm that it exists a solution to the equation f(x) = g(x) between x =3 and x =4 you should state the continuity of the functions.

1) Being f(x) a linear function means it is well defined between the points x = 3 and x =4 and you can conclude that it is a decreasing continuos function (decreasing because f(4) < f(3).

2) Being g(x) a ratonal functiion means that it is the ratio of two polynomials, g(x) = p(x) / m(x).Then, g(x) is continuous in the range [3,4] if and only if m(x) ≠ 0in the same range.

3) Given that you do not know whether m(x) meets that condition, you cannot conclude whether theres is a solution or not to f(x) = g(x).