f(x)= 7x+5; g(x)=x^2. Perform function operation of (f+g)(x) and find the domain.

Question

shadowfiend · Answer

First off, remember that $(f+g)(x) = f(x) + g(x)$.

So what is $f(x) + g(x)$ above?

anonymous · Answer

isn't it $$x^{2} +7x+5?$$

shadowfiend · Answer

Right-o.

shadowfiend · Answer

Now, what is the `domain' of a function?

anonymous · Answer

i read its the x-value.

shadowfiend · Answer

Right. So is there any value of x for which the equation above doesn't give an answer that makes sense?

anonymous · Answer

hmm?

shadowfiend · Answer

The range is all real numbers unless there is a value of x for which:

$$y = x^2 + 7x + 5$$

Gives an undefined y.

shadowfiend · Answer

(Hint: for this equation, there is no such value -- all numbers you plug in for x will give you a y value. So, the domain is all real numbers, or $(-\infty, \infty)$.

anonymous · Answer

so its all real numbers? so how do you know when an equation's domain is limited?

shadowfiend · Answer

Well, take the equation $y = \sqrt{x}$.

shadowfiend · Answer

If $x \lt 0$, then the square root is undefined -- it produces an imaginary number. So, the domain of the function is any value >= 0.

anonymous · Answer

i get it you can't have negatives in a square root. so its either a whole number or zero right?

shadowfiend · Answer

It's either a *positive* whole number or zero. Negatives are also whole numbers.

anonymous · Answer

okay i get it finally thanks a bunch!! you've been very helpful. :0]

shadowfiend · Answer

No problem, glad to help!