SOLUTION: Find the specified domain For f(x)=2x-5 and g(x)=&#8730;(x+6), what is the domain of f o g? This is how I worked it out but I am not sure this is correct. f(g(x))=2&#8730;

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Question 783530: Find the specified domain
For f(x)=2x-5 and g(x)=√(x+6), what is the domain of f o g?
This is how I worked it out but I am not sure this is correct.
f(g(x))=2√(x+6)-5
x+6=0
x=-6
Domain= (-∞, -6)∪(-6, ∞)
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
You are making the mistake of thinking "I cannot divide by zero, so set x+6 equal to zero to find the values of x that aren't allowed". This would work if the equation was y = 1/(x+6), but it's nothing like this

What you need to do is solve (see note below) for x to get

So the domain is really [-6, ∞)

Note: remember you cannot take the square root of a negative number, so that's why the radicand must be positive or 0, so that's why you must solve for x

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Nope. Your domain is all real numbers except for -6. Let's try -7: -7 + 6 = -1. But the radicand has to be non-negative. So:

Therefore

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

SOLUTION: Find the specified domain For f(x)=2x-5 and g(x)=&#8730;(x+6), what is the domain of f o g? This is how I worked it out but I am not sure this is correct. f(g(x))=2&#8730;

SOLUTION: Find the specified domain For f(x)=2x-5 and g(x)=√(x+6), what is the domain of f o g? This is how I worked it out but I am not sure this is correct. f(g(x))=2√