Question

已知f(x)=a*2^x+b*3^x. 若ab<0,则f(x+1)>f(x)时x的取值范围

Answer 1

f(x+1)-f(x)=a*2^(x+1)+b*3^(x+1)-(a*2^x+b*3^x)
=a*2^x+2b*3^x

令f(x+1)-f(x)=0
那么x=log(2/3)(-2b/a)

若a>0,解集是x<log(2/3)(-2b/a);
若a<0，解集是x>log(2/3)(-2b/a)

Answer 2

若a>0,x<log(-a/2b)/log(3/2);
若a<0,x>log(-a/2b)/log(3/2);