First, the domain name is -3.
1, f(x)=0, namely loga[( 1-x)(x+3)]=0.
Because 0 = loga (1);
So: loga [(1-x) (x+3)] = loga (1)
That is (1-x) (x+3) =1;
Finishing: x? +2x-2 = 0; Get: x 1=- 1-√3, x2 =-1+√ 3;
Both satisfy the domain -3
So the zero point of f(x) is-1√ 3;
2、f(x)=loga(-x? -2x+3)
The symmetry axis of the real number is x=- 1, so the real number increases at (-3,-1); Decreasing upward (-1,1);
Because 0
So f(x) decreases at (-3,-1); Increment to (-1,1);
So: f (x) min = f (-1) = loga (4) =-4.
So: a (-4) = 4.
Get: a=√2/2
I hope I can help you. If you don't understand, please hi me and wish you progress in your study!