Answer:
See explanations below
Step-by-step explanation:
Given the functions
f(x) = 12x - 12
g(x) = x/12 - 1
To show they are inverses, we, must show that f(g(x)) = g(f(x))
f(g(x)) = f(x/12 - 1)
Replace x with x/12 - 1 into f(x)
f(g(x)) =12((x-12)/12) - 11
f(g(x)) = x-1 - 1
f(g(x)) =x - 2
Similarly for g(f(x))
g(f(x)) = g(12x-12)
g(f(x)) =(12x-12)/12 - 1
12(x-1)/12 - 1
x-1 - 1
x - 2
Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other
First we would change the fractions into decimals and compare them. That way it would be easy to solve when needed.
1/2=0.50
5/8=0.625
1/8=0.125
Now we can see that 1/8 (0.125) is the smallest, followed by 1/2 (0.50), and 5/8 the largest. Now we can match the sizes with the insects.
Since the tiger beetle is the largest we will place that with the length of 5/8 since that is the largest.
The carpenter ant is second largest so it would be matched with 1/2
The aphid is the smallest so that would be with 1/8 as the smallest
*Hope that helped :D*
The formula is y=mx + b, or rearranged would be m= y/x -b/x.
