Function fx1 x gx x2 8x Find the domain of g fx use interval

Function:

f(x)=1/ x, g(x)= x² 8x

Find the domain of (g f)(x). (use interval notation)

Find the domain of (f g)(x). (use interval notation)

Find (f f)(x).

Find (gof)(x)

Find the domain of (f f)(x). (use interval notation)

Find (g g)(x).

f(x)=1/sqrtx , g(x)=x²-8x

For f(x), x cant be 0 or less than 0

Therefore domain of x=(0,infinity)

And gof(x)=g(f(x))=g(1/sqrtx)=(1/sqrtx)²-8(1/sqrtx)= 1/x - 8/sqrtx = (sqrtx -8x)/xsqrtx

Therefore domain of gof(x)=(0,infinity)

2. fog(x)=f(g(x))=f(x²-8x)=1/sqrt(x²-8x)

x²-8x should be greater than zero

x²-8x>0

x>8 or x<0

Therefore domain is (-infinity,0)U(8,infinity)