已知函数f(x)=3的x次方,且f(a+2)=18,g(x)=3的ax次方-4的x次方的定义域为[0,1]求:g(x)的单调区间g(x)的值域
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![已知函数f(x)=3的x次方,且f(a+2)=18,g(x)=3的ax次方-4的x次方的定义域为[0,1]求:g(x)的单调区间g(x)的值域](/uploads/image/z/1991633-41-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D3%E7%9A%84x%E6%AC%A1%E6%96%B9%2C%E4%B8%94f%EF%BC%88a%2B2%EF%BC%89%3D18%2Cg%EF%BC%88x%EF%BC%89%3D3%E7%9A%84ax%E6%AC%A1%E6%96%B9%EF%BC%8D4%E7%9A%84x%E6%AC%A1%E6%96%B9%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%5B0%2C1%5D%E6%B1%82%EF%BC%9Ag%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4g%EF%BC%88x%EF%BC%89%E7%9A%84%E5%80%BC%E5%9F%9F)
已知函数f(x)=3的x次方,且f(a+2)=18,g(x)=3的ax次方-4的x次方的定义域为[0,1]求:g(x)的单调区间g(x)的值域
已知函数f(x)=3的x次方,且f(a+2)=18,g(x)=3的ax次方-4的x次方的定义域为[0,1]
求:g(x)的单调区间
g(x)的值域
已知函数f(x)=3的x次方,且f(a+2)=18,g(x)=3的ax次方-4的x次方的定义域为[0,1]求:g(x)的单调区间g(x)的值域
f(a+2)=3^(a+2)=18
3^a=2
g(x)=3^ax-4^x=2^x-(2^x)²-1/4+1/4
=-(2^x-1/2)²+1/4
∵0≤x≤1
1≤2^x≤2
∴g(x)在[0,1]上单调递减
1/2≤2^x-1/2≤3/2
∴-2≤g(x)≤0
∴g(x)的值域为[-2,0]