Domains of Compositions

Examples

Find the domains of the compositions g(f) for 1 and 2; find the domains of the compositions f(g) for 3 and 4. Give the numerical values.

1.

f(x) = (x - 2)2 + 8, 1 <= x <= 5 g(x) = (1/2)(x - 10)2 + 3, 6 <= x <= 12 Answer

2.

f(x) = x2 + 1, all real x g(x) = sqrt[16 - x2], -4 <= x <= 4 Answer

3.

f(x) = |-x2 + 4|, -3 <= x <= 3 g(x) = x2 + 2, all real x Answer

4.

f(x) = sqrt(x + 1), -1 <= x <= 3 g(x) = 1/x, all real x except 0 Answer

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