Question

given functions f,g, and h find f o g o h state exact domain. show work

f(x)=1/x g(x)=lnx h(x)=2x+15

Answer 1

h has domain all reals
ln(n) has domain n > 0
so, we need 2x+15 > 0 or x > -7.5
1/x has domain x not zero.
Since ln(u) = 0 when u = 1, we need g(h) not 1.

So, ln(2x+15) cannot be 0.
That is, 2x+15 cannot be 1.
so, x cannot be -7

The domain of fogoh is thus all reals greater than -7.5 except -7

Answer 2

thank you my precalculus is now done - chemistry is next- can't wait!!