functions

f(x)=rad. x-9

write the intervals of the functions. How do I put the set of numbers in the form of intervals such as infinity.

I solved it and got the answer as this:
x < or = 9
(infinity,9]
Please help me, I am stuck.

(infinity,9]

means the interval's lower limit is at but excludes ∞. The exclusion is signified by the left parenthesis "(".
The upper limit is 9, and 9 is included, as indicated by the square bracker "]".

I do not quite understand the meaning of
f(x)=rad. x-9
so I cannot comment on whether the answer is correct.

To express the intervals in set notation, you have correctly identified that the interval can be written as "x ≤ 9." However, to include infinity in the interval, you need to use the symbol for infinity, which is represented by ∞.

To write the interval in set notation using infinity, you would use the following format:

(-∞, a] or [a, ∞)

In this case, since the function f(x) = √(x-9), you have found that x ≤ 9. So, to include infinity in the set notation, you would use:

(-∞, 9] or [9, ∞)

This notation indicates that x can be any real number less than or equal to 9, or it can be any real number greater than or equal to 9.

So, the correct interval for the function f(x) = √(x-9) would be (-∞, 9] or [9, ∞).