函数y=lg(sinxcosx)的单调递减区间是?A.(kπ-π/4,kπ+π/4) B.(kπ+π/4,kπ+π/2)C.(2kπ-π/4,2kπ+π/2) D.(kπ-π/4,kπ) (k∈Z)
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![函数y=lg(sinxcosx)的单调递减区间是?A.(kπ-π/4,kπ+π/4) B.(kπ+π/4,kπ+π/2)C.(2kπ-π/4,2kπ+π/2) D.(kπ-π/4,kπ) (k∈Z)](/uploads/image/z/15175567-55-7.jpg?t=%E5%87%BD%E6%95%B0y%3Dlg%28sinxcosx%29%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8F%E5%8C%BA%E9%97%B4%E6%98%AF%3FA.%EF%BC%88k%CF%80-%CF%80%2F4%2Ck%CF%80%2B%CF%80%2F4%29+B.%28k%CF%80%2B%CF%80%2F4%2Ck%CF%80%2B%CF%80%2F2%29C.%282k%CF%80-%CF%80%2F4%2C2k%CF%80%2B%CF%80%2F2%29+D.%28k%CF%80-%CF%80%2F4%2Ck%CF%80%29+%28k%E2%88%88Z%29)
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函数y=lg(sinxcosx)的单调递减区间是?A.(kπ-π/4,kπ+π/4) B.(kπ+π/4,kπ+π/2)C.(2kπ-π/4,2kπ+π/2) D.(kπ-π/4,kπ) (k∈Z)
函数y=lg(sinxcosx)的单调递减区间是?
A.(kπ-π/4,kπ+π/4) B.(kπ+π/4,kπ+π/2)
C.(2kπ-π/4,2kπ+π/2) D.(kπ-π/4,kπ) (k∈Z)
函数y=lg(sinxcosx)的单调递减区间是?A.(kπ-π/4,kπ+π/4) B.(kπ+π/4,kπ+π/2)C.(2kπ-π/4,2kπ+π/2) D.(kπ-π/4,kπ) (k∈Z)
复合函数问题.
设 f(x) = lg x,g(x) = sin x cos x
则y = f(g(x))
f(x)本身是单调递增函数,且定义域为x > 0.所以若要使f(g(x))单调递减,g(x)必须递减,且g(x) > 0.
g(x) = sin x cos x = (1/2) sin 2x
g(x)的递减区间为(kπ+π/4,kπ+3π/4); g(x) > 0的区间为(kπ,kπ+π/2)
二者相交,得到(kπ+π/4,kπ+π/2),
即B选项.
复合函数,LGX为递增函数,只需求SIN2X的减区间
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