SOLUTION: Consider the function h whose domain is the interval [−4, 4], with h defined on this domain by the formula h(x) = (2 + x)^2. Does h have an inverse? If so, find it, along

Algebra ->  Functions -> SOLUTION: Consider the function h whose domain is the interval [−4, 4], with h defined on this domain by the formula h(x) = (2 + x)^2. Does h have an inverse? If so, find it, along       Log On


   

Question 1067022: Consider the function h whose domain is the interval
[−4, 4], with h defined on this domain by the formula
h(x) = (2 + x)^2.
Does h have an inverse? If so, find it, along with its
domain and range. If not, explain why not.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
With [-4,4] for a domain,
h%28x%29=%282%2Bx%29%5E2 does not have an inverse,
because there is more than one x
for at least one value of y=h%28x%29 :
h%280%29=%282%2B0%29%5E2=2%5E2=4 and
h%28-4%29=%282%2B%28-4%29%29%5E2=%28-2%29%5E2=4 .

NOTE: f%28x%29=%282%2Bx%29%5E2 , with all real numbers as its domain,
has a graph that looks like this:
graph%28240%2C300%2C-6%2C2%2C-1%2C9%2C%282%2Bx%29%5E2%29 ,
so to have an inverse,
the domain cannot include at the same timex
values to the left and right of x=-2 .