FUNCTION. Let f(x)=1/(x-4) and g(x)=7/x+4, find 1) f(g(x)) 2)g(f(x))?
回答 (2)
2013-06-28 2:15 am
1) f(g(x) =
1/({7/(x + 4)} - 4) =
(x + 4)/(7 - 4(x + 4)) =
(x + 4)/(7 - 4x - 16) =
(x + 4)/(-4x - 9) =
-(x + 4)/(4x + 9)
2)g(f(x)) =
7/({1/(x - 4)} + 4) =
7(x - 4)/(1 + 4(x - 4)) =
(7x - 28)/(1 + 4x - 16) =
(7x - 28)/(4x - 15)
1/({7/(x + 4)} - 4) =
(x + 4)/(7 - 4(x + 4)) =
(x + 4)/(7 - 4x - 16) =
(x + 4)/(-4x - 9) =
-(x + 4)/(4x + 9)
2)g(f(x)) =
7/({1/(x - 4)} + 4) =
7(x - 4)/(1 + 4(x - 4)) =
(7x - 28)/(1 + 4x - 16) =
(7x - 28)/(4x - 15)
2013-06-28 2:07 am
f(g(x)) = 1/(7/x + 4 - 4) = 1/(7/x) = x/7
g(f(x)) = 7/(1/(x - 4)) + 4 = 7x - 28 + 4 = 7x - 24
g(f(x)) = 7/(1/(x - 4)) + 4 = 7x - 28 + 4 = 7x - 24
收錄日期: 2021-04-30 23:57:08
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