Sol 1 Let . Then , so and therefore .
Sol 2 Let . Then , so and . Thus .
Sol 3 Let , so and . Then , so . The domain of is the same as the range of , so it is the interval
since the graph of f is the top half of the parabola .
Sol 4 Let . Then , so
Sol 5 Setting , for example, and then solving for gives ; so is not 1-1 and therefore does not have an inverse.
Sol 6 Let ; then , so adding 4 to both sides gives and therefore . Taking square roots of both sides, using the fact that so , gives and so . Therefore . The domain of is the range of , which is the interval since for .
Sol 7 To find , we must solve the equation for :
since . Therefore .
Sol 8 Let .
The domain of is the same as the range of . Since for , for . Furthermore, if , then and therefore ; so the domain of is ,the range of .
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