First, find an expression for g(x):
[tex]\begin{gathered} f(x)=\log _2(x) \\ g(x)=-f(x)-1 \\ =-\log _2(x)-1 \end{gathered}[/tex]
The x-intercept of g(x) is a number such that g(x)=0. Then:
[tex]\begin{gathered} -\log _2(x)-1=0 \\ \Rightarrow-1=\log _2(x) \\ \Rightarrow\log _2(x)=-1 \\ \Rightarrow x=2^{-1} \\ \Rightarrow x=\frac{1}{2} \end{gathered}[/tex]
Then, the coordinates of the x-intercept are:
[tex](\frac{1}{2},0)[/tex]
The domain of g is the set of all values that x can take. The domain of a logarithm is the set of all positive numbers. Then, the domain of g is:
[tex](0,\infty)[/tex]
The y-intercept is the value of the function when x=0. Since 0 is not in the domain of g, then, g does not have a y-intercept.
