Determine the domain of fx Give your answer using interval n

Determine the domain of f(x). Give your answer using interval notation. F(x) = {2/x^2 - 22x +120 if 4 lessthanorequalto x lessthanorequalto 11 3x - 8 if x > 11 Domain: ___________

Solution

for x>11 , f(x) is always defined

for 4<=x<=11, f(x) is not defined when:
x^2 - 22x + 120 =0
x^2 - 10x -12 x +120 = 0
x (x-10) -12 (x-10) = 0
(x-10)(x-12) = 0
x=10 and x=12
but only x=10 lies in 4<=x<=11
so, function is not defined for x=10

domain is
[4,inf) - {10}