All domains must be in INTERVAL NOTATION fx x2 12 gx Squa

All domains must be in INTERVAL NOTATION f(x) = x^2 + 12, g(x) = Squareroot x - 1 (f - g) (2) = (fg)(1) = (f(g(x)) = g(f(x)) = Domain of f(x) = Domain of g(x) = Domain of f(x) = 2x + 1/2x^2 - 50 Domain of f(x) = log_3 (2x + 5) - 4

Solution

f(x)=x²+12          g(x)=sqrt(x-1)

1. (f-g)(2)

(f-g)(x)= x²+12 - sqrt(x-1)

(f-g)(2)= 2²+12 -sqrt(2-1)= 4+12-1=15

2. (fg)(1)

(fg)(x)= (x²+12)sqrt(x-1)

(fg)(1)= (1²+12)sqrt(1-1) = 0

3. f(g(x))= f(sqrt(x-1)) = (sqrt(x-1))²+12= x-1+12= x+11

4. g(f(x))= g(x²+12) = sqrt(x²+12 -1)= sqrt(x²+11)