Question

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]

Answer 1

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]