SOLUTION: What's the domain of f+g when f(x)=2x-5 and g(x)= square root x+6

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Question 285588: What's the domain of f+g when f(x)=2x-5 and g(x)= square root x+6
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
(f+g)(x) = f(x) + g(x)

f(x) = 2x-5
g(x) = sqrt(x+6)

(f+g)(x) = (2x-5) + sqrt(x+6)

The only restriction on the domain of this function is the square root of (x+2^ can't be negative.

to find out when sqrt(x+6) goes negative, use the equation:

(x+6) < 0

Subtract x from this equation to get x < -6

When x < -6, the square root of (x+6) goes negative and the domain goes invalid.

The domain of (f+g)(x) is therefore all values of x >= -6

Note that this i also the domain of g(x).

The domain of f(x) is all real value of x.

(f+g)(x) adds f(x) plus g(x) together so the domain becomes the more restrictive of the two which is the domain of g(x).

A graph of the equation (f+g)(x) = (2x-5) + sqrt(x+6) is shown below:

graph+%28400%2C400%2C-10%2C10%2C-20%2C20%2C%282x-5%29+%2B+sqrt%28x%2B6%29%29

You can see that the graph stops at x = -6 and doesn't go any further.

That's because the value of y when x < -6 is not a real number and is therefore undefined.