Question

find the domain of fg f(x) = x^2+1 g(x)= 1/x


a.
all real numbers
c.
all real numbers, except -1
b.
all real numbers, except 0
d.
all real numbers, except 1

Answer 1

B. All real numbers, except 0.

when you plug in the function f in g we get

fg=1/(1/x^2+1).

now, if you plug in -1,1 as the inputs of X then the fg is rational/real., then the domain of fg is all real numbers with some special dope case. note that when you plug in 0, it's invalid/the expression approaches infinity(1/0=infinity). thus, we neglect 0 and include all real numbers except 0 for the domain of fg. hope this helps. if you find any mistakes please do Lemme know cuz I love making mistakes and learning from them! thank you !