Question

Find the domain and range of f(x)= 3/x-3​

Answer 1

Answer:

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve 3−x=0⇒x=3←excluded value

⇒domain x∈R,x≠3

x∈(−∞,3)∪(3,∞)←in interval notation

f(x)=3+x3−x

divide terms on numerator/denominator by x

f(x)=3x+xx3x−xx=3x+13x−1

as x→±∞,f(x)→0+10−1=−1←excluded value

⇒range y∈R,y≠−1

y∈(−∞,−1)∪(−1,∞)

graph{(3+x)/(3-x) [-10, 10, -5, 5]}