SOLUTION: Consider the function h whose domain is the interval [−3, 3], with h defined on this domain by the formula h(x) = (3 + x)^2. Does h have an inverse? If so, find it, along

Algebra ->  Functions -> SOLUTION: Consider the function h whose domain is the interval [−3, 3], with h defined on this domain by the formula h(x) = (3 + x)^2. Does h have an inverse? If so, find it, along       Log On


   

Question 942368: Consider the function h whose domain is the interval
[−3, 3], with h defined on this domain by the formula
h(x) = (3 + x)^2.
Does h have an inverse? If so, find it, along with its
domain and range. If not, explain why not.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
In that domain, h has an inverse. h takes a value at -3 and up to 3 for x. The interval of h [-3, 0] gets an inverse but the interval [0, 3] gets a different inverse.

%28y%2B3%29%5E2=x
y%2B3=0%2B-+sqrt%28x%29
y=-3%2B-+sqrt%28x%29-------the inverse relation, TWO branches.

The left branch of h has the inverse y=-3-sqrt%28x%29
domain of y [0, 9] and range from -3 to 0 or [-3, 0].
Notice how the domain and range for h become switched in the inverse.

Similar happens with the other branch.

graph%28300%2C300%2C-7%2C7%2C-7%2C7%2C-3-sqrt%28x%29%2C-3%2Bsqrt%28x%29%29