obtain the domain and range of ln(g(x))??
g(x)=6+4x-2x2
Hi
g(x)=-2x²+4x+6 = -2(x+1)(x-3)
It must be strictly positive because ln(a) is defined for a>0
The domain is therefore ]-1,3[
g(x)=-2x²+4x+6 is a parabola oriented towards negative y
Maximum is obtained for x=1 and g(1)=8
Range is therefore ]-oo,3ln(2)]
OK
ln(g(x)) is defined on ]-1,3[
On ]-1,3[ g(x) is increasing between -1 and 1 and decreasing between 1 and 3
Therefore ln(g(x)) is increasing between -1 and 1 and decreasing between 1 and 3
g(-1)=0 => ln(g(x)) has -oo for limit in -1
g(1)=8 => ln(g(1)) = ln(8) = ln(2^3) = 3 ln(2)
g(3)=0 => ln(g(x)) has -oo for limit in 3