Find the domain of the following function f(x)=[x]+ x
Answers
y=f(x).
We can try and motivate how to find this with an example. Let's try to find the range of:f(x)=x2+1So we want to find y-values such that there is some x where y=x2+1. Suppose we want to check if y=5 is in the range of f(x). Then, we want to check if there is an x-value such that x2+1=5. We can solve this equation as follows:x2+1=5x2=4x=±2So since either x=2 or x=−2 works, we know that y=5 is in the range of f(x).
More generally, if we want to find the full range of y=x2+1, we can solve for x (taking the inverse of the function) to get x=√y−1. Then, the range of f(x) is simply the domain of √y−1, because these are all the values where there is some x-value with f(x)=y. In this example, the domain of √y−1 is just all values where y−1≥0, so [1,∞) is the range of f(x)=x2+1.
Overall, the steps for algebraically finding the range of a function are:
Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x).
If you can't seem to solve for x, then try graphing the function to find the range.
Common functions and their ranges
Below, we can list a few common functions and the ranges they have. This will help you find the range of more complicated functions without having to do all the steps above.
1. f(x)=|x|. The range of f(x) is [0,∞), which is all non-negative real numbers.
2. f(x)=ln(x). The range of f(x) is (−∞,∞), which is all real numbers. In fact, this range holds for any base for the log.
3. For a>0 and a≠1, f(x)=ax has a range of (0,∞).
Answer:
i sadly do not know
Step-by-step explanation: