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

First off, remember that $$(f+g)(x) = f(x) + g(x)$$. So what is $$f(x) + g(x)$$ above?

2. anonymous

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

Right-o.

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

5. anonymous

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

7. anonymous

hmm?

The range is all real numbers unless there is a value of x for which: $y = x^2 + 7x + 5$ Gives an undefined y.

(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 $$(-\infty, \infty)$$.

10. anonymous

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

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

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.

13. anonymous

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

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

15. anonymous

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