Question

已知f(x)=-2x+1求满足f(a²+1)>f(5)的实数,a的取值范围

Answer 1

已知

f(x)=-2x+1

f(a^2+1) >f(5)

-2(a^2+1) +1 > -2(5)+1

-2a^2-1 > -9

2a^2<8

a^2<4

-2<a<2

a的取值范围 :-2<a<2

Answer 2

f'(x)=-2<0,即，x越小，f(x)值越大
因为，f(a²+1)>f(5)
所以，a²+1<5,即a²<4
所以，-2<a<2