given f(x) = x^2 - 3x + 5 and g(x) = x-2, find the composite function (f o g)(x) and simplify
simplify (8+3i)^2 and write the answer in the form of a = bi, where a and b are real numbers
2007-05-02 03:45:37 · 2 answers · asked by Michael S 1 in Science & Mathematics ➔ Mathematics
The (f°g) notation is always a bit vague, since some people use it to mean g(f(x)) and others use it to mean f(g(x)). I'm going to guess that you mean f(g(x) (since the result is more interesting.
Since g(x) = x-2, then f(g(x)) just means to substitute x-2 everywhere in f that x appears.
(x-2)² - 3(x-2) + 5 Expanding:
x² - 4x + 2 - 3x + 6 + 5 Collect terms:
x² - 7x + 13 Done.
(8 + 3i)² = 64 + 48i + 9i² and since i² = -1
64 - 9 + 48i = 55 + 48i is the answer.
HTH
Doug
2007-05-02 03:55:51 · answer #1 · answered by doug_donaghue 7 · 1⤊ 0⤋
fog(x)=f(g(x))=(x-2)² - 3(x-2) + 5
(8 + 3i)²=8*8 + 2*8*3i + 3*3i² = 8*8 + 2*8*3i - 3*3
55= - 48i
2007-05-02 10:52:33 · answer #2 · answered by alan turing 1 · 0⤊ 0⤋