Question

求值域 求大神解答

Answer 1

4
令t=sinx
指数g(t)=t^2+3t; -1≤t≤1
抛物线g(t)开口向上对称为t= - 3/2,
函数g(t)在[-1,1]上单调增，
g(-1)≤g(t)≤g(1)
-2≤g(t)≤4
y=2^(g(t))
1/4≤y≤16
5
令t=log2(x)
1≤t≤2
log4(x)=[log2(x)]/[log2(4)]=t/2
y=t^2/2
抛物线y(t)开口向上，对称轴：t=0
函数y(t)在[1,2]上单调增，
y(1)≤y≤y(2)
1/2≤y≤2
6
令t=lnx,==>1≤t≤2
y=t/(t+1)
t=yt+y
(1-y)t=y
t=y/(1-y)
1≤t≤2
-2≤y/(y-1)≤-1
{y/(y-1)≤-1
{y/(y-1)≥-2
==>
{(2y-1)/(y-1)≤0
{(3y-2)/(y-1)≥0
==>
{(y-1)(2y-1)≤0 (y≠1)
{(y-1)(3y-2)≥0 (y≠1)
==>
{1/2≤y<1
{y>1,或y≤2/3
1/2≤y≤2/3