We are given the following two functions
[tex]\begin{gathered} f(x)=\frac{1}{x-4} \\ g(x)=\frac{1}{x}-3 \end{gathered}[/tex]
Let us evaluate the functions on the given points.
a. f(1/4)
Substitute x = 1/4 into the function f(x)
[tex]f(\frac{1}{4})=\frac{1}{\frac{1}{4}-4}=\frac{1}{\frac{1-4\cdot4}{4}}=\frac{1}{\frac{1-16}{4}}=\frac{1}{\frac{-15}{4}}=-\frac{4}{15}[/tex]
Therefore, f(1/4) = -4/15
b. g(1/4)
Substitute x = 1/4 into the function g(x)
[tex]g(\frac{1}{4})=\frac{1}{\frac{1}{4}}-3=4-3=1[/tex]
Therefore, g(1/4) = 1
c. f(-1/3)
Substitute x = -1/3 into the function f(x)
[tex]f(-\frac{1}{3})=\frac{1}{-\frac{1}{3}-4}=\frac{1}{\frac{-1-3\cdot4}{3}}=\frac{1}{\frac{-1-12}{3}}=\frac{1}{\frac{-13}{3}}=-\frac{3}{13}[/tex]
Therefore, f(-1/3) = -3/13
d. g(-1/3)
Substitute x = -1/3 into the function g(x)
[tex]g(-\frac{1}{3})=\frac{1}{-\frac{1}{3}}-3=-3-3=-6[/tex]
Therefore, g(-1/3) = -6
