To determine the y intercept of a function we need to remember that it happens when x=0; plugging this value in the expression for the function we have:
[tex]\begin{gathered} f(0)=\log_(2-0)\sqrt{0+3} \\ f(0)=\sqrt{3}\log2 \end{gathered}[/tex]Therefore, the y-intercept is
[tex](0,\sqrt{3}\log2)[/tex]To determine the x intercept we need to remember that this happens when the value of the function is zero, then we equate the expression to zero and solve for x:
[tex]\log(2-x)\sqrt{x+3}=0[/tex]Now, we know that a product is zero only if one of the factors is zero, then this equation leads to the following two equations:
[tex]\begin{gathered} \log(2-x)=0 \\ \sqrt{x+3}=0 \end{gathered}[/tex]Solving the first one we have:
[tex]\begin{gathered} \log(2-x)=0 \\ 2-x=10^0 \\ 2-x=1 \\ x=2-1 \\ x=1 \end{gathered}[/tex]Solving the second equation we have:
[tex]\begin{gathered} \sqrt{x+3}=0 \\ x+3=0 \\ x=-3 \end{gathered}[/tex]Therefore, the x-intercepts are (-3,0) and (1,0)