Let f(x) = 2x +1 and g(x) = sqrt of x. 1) Find the domain of f/g. 2) Find the domain of g/f.

Question

Let f(x) = 2x +1 and g(x) = sqrt of x. 1) Find the domain of f/g. 2) Find the domain of g/f.

Answer 1

f(x)=2x+1

g(x) = sqr(x)

f/g = f(x)/g(x) = (2x+1)/sqr(x)

domain of f/g is all real numbers except x=0

in interval notation (-infinity,0)U(0,infinity)

x=0 makes the deminator =0 whick makes f/g undefined

g/f = g(x)/f(x) = sqr(x)/(2x+1)

domain of g/f is x>0

[0,infinity)

x<0 makes g/f imaginary

also x=-1/2 makes g/f undefined