Domain of composite function example:
Domain for : Step 1 Domain for is all x so that x + 10
So we need .
Step 2 Output for g becomes input for f so we must find the range of g.
Graph g to see that range of g is . Step 3 Find domain of f. All x so that
Notes for Section 5.6
Find a polynomial of degree 6 whose coefficients are real numbers and has the zeros 2, -3, 2i,
By the Conjugate Pairs Theorem, since 2i is a zero, then -2i is too and since 1 2i is a zero,
then 1 + 2i is as well. This gives us
Notes for Section 5.5
Using the function , we apply the material in the section.
Bounds on real zeros: means (1) first divide all coefficients by the leading coefficient to get x4
+(1/2)x3 (7/2)x2 (3/2)x + (3/2)
Now find the bound. Choose the largest of t