Domain l(x) is
-12 less than or equal to x less than equal to 12
and it's range is
0 less than or equal to l(x) less than equal to 3
(b) What are the domain and range of
l(1/5x)
Enter the exact answer
Domain
Range
To find the domain and range of the function l(1/5x), we need to consider the restrictions placed on the original function l(x) and how they would transfer to the new function.
For the domain, we need to find all the possible values of x that can be plugged into the function l(1/5x). Based on the given restrictions for the original function:
-12 ≤ x ≤ 12
To find the new domain, we substitute the expression 1/5x into the above inequality:
-12 ≤ (1/5x) ≤ 12
To simplify the inequality, we can multiply all the terms by 5 to remove the fraction:
-60 ≤ x ≤ 60
Therefore, the domain of the function l(1/5x) is:
-60 ≤ x ≤ 60
Now let's move on to finding the range. Since the range of the original function l(x) is given as:
0 ≤ l(x) ≤ 3
We can substitute the expression l(1/5x) into this inequality:
0 ≤ l(1/5x) ≤ 3
Since the range is determined by the values of l(1/5x), which are also determined by the values of x, the range of the function l(1/5x) remains the same:
0 ≤ l(1/5x) ≤ 3
Therefore, the range of the function l(1/5x) is:
0 ≤ l(1/5x) ≤ 3
To summarize:
Domain: -60 ≤ x ≤ 60
Range: 0 ≤ l(1/5x) ≤ 3