What are the domains for these equations ....?

Question

Domain of graphs and equations : HELP!!!! What are the domains for these equations ....?

f (x) = log (x + 6) + log (x − 3)

g (x) = 3^(x+1) − 3^(x-1)

h (x) = sqrt(x − 2)² - 3

k (x) = −4x² + 5x

r (x) = x + √x

What are the domains for Df , Dg, Dh, Dr , Dg/k

Answer 1

Df is x>3

g (x) = 3^(x+1) − 3^(x-1)

g (x) = (3^x)(3 - 1/3)

Dg is all x

Dh is all x

Dr is x > 0

g/k = (3^x)(3 - 1/3)/(x(5 - 4x)

Dg/k is x ≠ 0, x ≠ 5/4