# Thread: find (f + g) (x) and its domain

1. ## find (f + g) (x) and its domain

f(x) = 1 / squarroot(x)
g(x) = x^2 - 4x

how do i begin?

2. $\displaystyle (f+g)(x) = \frac{1}{\sqrt{x}} + x^2 + 4x$

What values can't you plug into the function?

3. 0
or anything negative?

4. So your domain: $\displaystyle x > 0$ .. i.e. non-zero and non-negative values.

5. Wow, so then (f/g)(x) would have the same domain?

And so would (fog)(x)
And so would (f + g)(x)

for these same values of g and f???
f(x) = 1 / squarroot(x)
g(x) = x^2 - 4x

6. $\displaystyle (\tfrac{f}{g})(x) = \frac{\frac{1}{\sqrt{x}}}{x^2 - 4x} = \frac{1}{\sqrt{x} \left(x^2 - 4x\right)} = \frac{1}{x\sqrt{x}(x-4)}$

There's an extra restriction here. Remember, can't have a division by 0.

$\displaystyle (f \circ g)(x) = f(g(x)) = f(x^2 + 4x) = \frac{1}{\sqrt{x^2 + 4x}}$

Just like earlier analysis, we can't have a division by 0 nor a square root of a negative number. So, our domain is restricted to values such that: $\displaystyle x^2 + 4x > 0$