Find the range of the function for the domain(-4,-2,0, 1.5,4).f(x) = 5x²+ 4
1 answer:
<h2>Hello!</h2>
The answer is:
The range or output for the given domain is:
(84,24,4,15.25,84)
<h2>Why?</h2>To find the range (output) for the given domain (inputs) we need to evaluate the given function with the given inputs or "x" values.
So, evaluating, we have:
- Range with "x" equal to -4:
- Range with "x" equal to -2:
- Range with "x" equal to 0:
- Range with "x" equal to 1.5:
- Range with "x" equal to 4:
Hence, the range or output for the given domain is:
(84,24,4,15.25,84)
Have a nice day!
You might be interested in
Hi, you haven't provided the programing language in which you need the code, I'll explain how to do it using Python, and you can follow the same logic to make a program in the programing language that you need.
Answer:
import math
def rectangle(perimeter, area):
l1_1 = (perimeter+math.sqrt((perimeter**2)-(16*area)))/4
l1_2 = (perimeter-math.sqrt((perimeter**2)-(16*area)))/4
l2_1 = area/l1_1
l2_2 = area/l1_2
print(l1_1,l2_1)
print(l1_2,l2_2)
if l1_1.is_integer() and l2_1.is_integer() and l1_1>0 and l2_1>0:
return(int(max(l1_1,l2_1)))
elif l1_2.is_integer() and l2_2.is_integer() and l1_2>0 and l2_2>0:
return(int(max(l1_2,l2_2)))
else:
return(None)
Explanation:
- We import math to make basic operations
- We define the rectangle function that receives perimeter and area
- We calculate one of the sides (l1_1) of the rectangle using the quadratic equation to solve 2h^2 - ph + 2a = 0
- We calculate the second root of the quadratic equation for the same side (l1_2)
- We calculate the second side of the rectangle using the first root on w = a/h
- We calculate the second side of the rectangle using the second root on w= a/h
- We verify that each component of the first result (l1_1, l2_1) is an integer (using the build-in method .is_integer) and greater than 0, if True we return the maximum value between them (using the max function) as w
- If the first pair of sides evaluate to False we check the second root of the equation and if they meet the specification we return the max value
- if all the if statements evaluate to false we return None to indicate that not positive or integer sides were found
