Given f(x) find:

Question

Given f(x) = 1/x-2 and g(x) = sqrt(x+3):

 

1.) Find f(g(x)) and DO NOT rationalize the denominator:

 

 

 

 

2.) Find the domain of f(g(x)):

 

 

Answer 1

f(g(x)) = 1/(√(x + 3) - 2

 

What's underneath the radical has to be positive, so...

 

x + 3 > 0

x > -3

 

The denominator can't equal 0.

 

√(x + 3) - 2 ≠ 0

√(x + 3) ≠ 2

x + 3 ≠ 4

x ≠ 1

 

So, the domain is x > -3, x ≠ 1