Can someone please explain and solve why the domain is diffe

Can someone please explain and solve why the domain is different in these two problems?

Solution

a) f(x)=⁷(x²-4x-21)

domain of f(x) is (-,)

b) f(x)=¹⁰(x²-4x-21)

x²-4x-21>=0

(x+3)(x-7)>=0

x<=-3 ,x>=7

domain of f(x) is (-,-3]U[7,)

for f(x)=ⁿg(x)

when n is odd , f(x) is defined for all real numbers of g(x)

when n is even , f(x) is defined only for non negative numbers of g(x)