Question

Help how do I do this??
find domain for f+g(x)
f(x)=1/x-3 g(x)=2x+4

Answer 1

is that f(x) + g(x)?

Can you show me what f(x) + g(x) equals

Answer 2

or rather express it in a way in which we can find its domain

Answer 3

@Australopithecus it just asked for the domain of f(x) + g(x)
and all that is given is f(x)=1/x-3 g(x)=2x+4

Answer 4

you solve f and then you solve g and then you get the solutions and then you get ur answer

Answer 5

so the solution is the domain? @peanutbutter817

Answer 6

first off you need to understand function notation.

f(x) is just another way of writing y, but it provides more information because you can use it to designate a point in a function readily by simply replacing x with a number for example:

y = x + 3
can be represented as,
f(x) = x + 3

when we say f(3)

we simply mean

f(3) = 3 + 3

just realize that,

f(x) is the same as writing x + 3

so if you have,

f(x) + g(x)

where,
f(x) = x + 3
and
g(x) = 2 + x

f(x) + g(x) = (X + 3) + (2+x)

Answer 7

once you solve each g and f plug them in f(x)+g(x)and then you will get your answer
@eragon4

Answer 8

once you write out what f(x) + g(x) is in the case of your problem you can look for the domain, the domain is simply the numbers that can be inputed as x in your equation.

You have to remember simple rules to recognize what numbers cannot be inputed into your function (and thus figure out what your domain is).

Rules:
1. You cannot divide by 0, meaning zero cannot be in the denominator, it can be in the numerator though, in which case the fraction always equals 0)
To clarify:
3/0 = undefined
3/(3-3) = undefined
0/0 = undefined
0/3 = 0

2. In the case of radicas (numbers raised to the power of a fraction) you cannot have a negative number under them you can have 0 though, as this will give you imaginary numbers (The domain is simply concerned with what real numbers are allowed).
To clarify:
\[\sqrt{-1} = Imaginary Number\]
\[-3^\frac{1}{3} = Imaginary Number\]
etc.

3. When dealing with logrithems such as log(x) or ln(x), x cannot be less than or equal to 0
To clarify:
Recognize that
log(x) = y
is the same as
10^y = x

in this case you should be able to recognize that in 10^y = x, there is no number you can input into y that will make x equal to or less than zero

Answer 9

I recommend studying what I wrote above then we can go over the problem together, all I ask is you express, f(x) + g(x) in the way I specified above