Consider the function f(x)=x^2 and g(x)=√x. Find the domain of f/g. Explain every step.

Question

Give each step in order and tell why each step was taken to get the answer. g(x)=sqrt of x. 

Answer 1

The domain of a rational function - one with a variable in the denominator is the value of the variable that makes the fraction undefined.

in this case g(x) is the denominator and whatever makes it 0 or undefined is not allowed to be in the domain

sqrt(x) >0

if x = 0, the square root of 0 is 0 and the denominator is not allowed to be 0

If x<0 then the square root of x is not a real number

 

the domain is x>0   or   (0, infinity)