Compositions of two functions

Question

f(x)=x²-5

g(x) = sqr root of x-6

 

Find the composition f*g and specify its domain using interval notation

 

(f*g)(x)=?

Domain of f*g=? 

Answer 1

f(x)=x²-5

g(x)=√(x-6)

(f*g)(x)=f(g(x))=(g(x))²-5=(√(x-6))²-5=x-6-5=x-11

Domain: D((f*g)(x))=R=(-∞, +∞)