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
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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) (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.
-------the inverse relation, TWO branches.
The left branch of h has the inverse
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.
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