# Thread: [SOLVED] Domain and range

1. ## [SOLVED] Domain and range

Describe the domain range of f and g. form the function f(g(x)) and describe the domain and range of this composed function.

F(x)=sqrtX G(x) = x+5

i really need help with this i dont really understand domain and range

2. Originally Posted by john doe
Describe the domain range of f and g. form the function f(g(x)) and describe the domain and range of this composed function.

F(x)=sqrtX G(x) = x+5

i really need help with this i dont really understand domain and range
Keep in mind that the domain and range of $\displaystyle \sqrt{x}$ is $\displaystyle \left[0,\infty\right)$

The domain and range of $\displaystyle x+5$ is $\displaystyle \left(-\infty,\infty\right)$

If $\displaystyle f(x)=\sqrt{x}$ and $\displaystyle g(x)=x+5$, then $\displaystyle f(g(x))=\sqrt{x+5}$

Keep in mind that $\displaystyle \sqrt{x+5}$ exists when $\displaystyle x+5>0$. Solve this for x, and this will give you the domain [convert it to interval notation, though]

The range would be all values of $\displaystyle y>0$. No value of x will cause this square root function to be negative. Rewrite this in interval notation as well.

I hope this makes sense!

--Chris

3. I understand the domain and range. What i don't get is, the product of squaring any number would give me two answer so f(g(x)) wouldn't be a function. ex: if i square 4 wouldn't i get + or - 2.

4. Originally Posted by john doe
I understand the domain and range. What i don't get is, the product of squaring any number would give me two answer so f(g(x)) wouldn't be a function. ex: if i square 4 wouldn't i get + or - 2.
no, if you square 4 you get 16. what you are getting at is the square-root of 4. in that case the answer is 2. only 2, -2 is not $\displaystyle \sqrt{4}$. since $\displaystyle \sqrt{x} \ge 0$ for all $\displaystyle x \in \mathbb{R}$

definitions that always seem to help me:

the domain is the set of input values (in this case, x values) for which a function is defined, or has an output value.

the range is the set of output values (in this case, y-values)

so just figure out what x-values work in your function, and that's your domain. it is often easier to find what does not work, and say the domain is the set of all values but those that don't work. the range is the set of outputs you can obtain by plugging in any one of these domain values

hope that helps