Find the domain of the function. Show all work.
1 if -9 < or = x<-7
f(x)= Abs(x) if -7 < or = x<9
Sq root(x)if 9 < or = x < or=35
Looks like the function is defined for all values of x in [-9,35]. That would be the domain.
It's a lot easier to read if you say
f(x) =
1 if -9 <= x < -7
abs(x) if -7 <= x < 9
sqrt(x) if 9 <= x <= 35
Beth,please check your 19-23-11,6:24pm
post.
To find the domain of the given function, we need to determine the values of x for which the function is defined.
Let's analyze each segment of the function:
1. For the first segment, the function is defined as 1 when -9 ≤ x < -7. This means that any value of x between -9 and -7 (including -9 but excluding -7) will have a corresponding value for f(x). Therefore, the domain for this segment is -9 ≤ x < -7.
2. For the second segment, the function is defined as the absolute value of x when -7 ≤ x < 9. This indicates that any value of x between -7 and 9 (including -7 but excluding 9) will have a corresponding value for f(x). Thus, the domain for this segment is -7 ≤ x < 9.
3. For the third segment, the function is defined as the square root of x when 9 ≤ x ≤ 35. This implies that any value of x between 9 and 35 (including both 9 and 35) will have a corresponding value for f(x). Therefore, the domain for this segment is 9 ≤ x ≤ 35.
Combining all three segments, we have the overall domain of the function as the union of the individual domains:
Domain: -9 ≤ x < -7, -7 ≤ x < 9, 9 ≤ x ≤ 35