Question

if i want to find the domain of 5^(2x-1) +25^(2x-0.5) +5^(x-1) i have to work out x value ? if so i came so far as 5^(5x) = 0 how can i come to the value of x?

Answer 1

Lindie, you are definitely confused about the definition of domain.

Answer 2

ok so what must i do to get the domain of this exponential formula?

Answer 3

The domain of a function is not "What is the x value." A function does not have a SPECIFIC x-value that is THE x-value.
No, a function takes in any number of x-values, any number of inputs, and depending on what you put in, it gives an output, a y-value.

Domain is not asking "What is THE x-value?"
Domain is asking "What are ALL of the POSSIBLE x-values?"

Answer 4

ok thanks how do you get the possible x values ?

Answer 5

Well, let me start by giving you some examples where we leave certain x values out of our domain. The reason we will leave a particular x value out of the domain is because, if we plug in that x-value, we do not get an output.

The first example function is:
f(x) = \(\sqrt{x}\)
If I plug in x=4, I get an output of y=2
If I plug in x=9, I get an output of y=3
If I plug in x=2, I don't get a nice, neat answer, but I get an infinite decimal, y=1.41421...
If I plug in x=0, I get an output of y=0
So far, every x value input has given me a y value output that I can calculate. All of these x values would be in the domain.
But what about x=-1? \(\sqrt{-1}\) does not have a normal real answer, so as long as I only care about real numbers, there is no output. We've run into the first x value that is NOT in the domain.

Answer 6

And in general, for that function, any negative number for x would not allow me to calculate an output. So the domain would be \(x\ge0\).

Another example would be
\(\Large g(x) =\frac{1}{x}\)
For almost any x value you put in, you can calculate an ouput. There is only one value that causes you trouble. Which value is not in the domain for this function?

Answer 7

any negative value

Answer 8

For my second example? Well, if you give me x=-1, I would plug in and calculate y = \(\frac{1}{-1} = -1\)
So there's at least one negative x value that gives me an output, which means it must be in the domain.

Answer 9

ok so i must replace the x values until it doesn't give me a value ?
x>0

Answer 10

That's a good way to think about it. As you get used to different functions, it will be easier to anticipate what kinds of things won't give you a y-value.
In my first example, we had a square root function. We can't square root negatives, so any x-value that causes you to square root a negative would not be in the domain.
In my second example, we divided by x. Since we can't divide by 0, the domain would be any real number except 0.

Answer 11

In your problem, we're doing exponents of 5 and 25, then adding those results together. What kinds of numbers are those exponents allowed to be?
Can you have a positive exponent? Can you have a 0 exponent? Can you have a negative exponent? Fractions? Decimals?

Answer 12

is the domain of the question( -3/5 : infinity)

Answer 13

Let me ask again:
What kinds of numbers are those exponents allowed to be?
Can you have a positive exponent? Can you have a 0 exponent? Can you have a negative exponent? Fractions? Decimals?

Experiment with this in your calculator if you need to. Put in 5 and then different kinds of exponents. See if it gives you an answer or an error.

Answer 14

(Sorry for not telling if your answer is right or wrong. I'd rather you understand the concept well enough to be able to tell me confidently on your own whether it is or not.)