1.函數(shù)y=以a為底X-2的對(duì)數(shù)的圖像恒過定點(diǎn)?2.函數(shù)f(x)=以十為底(x-1)+(根號(hào)下四減x)的對(duì)數(shù)的定義域?
3.函數(shù)y=以a為底(2x+1)/(x-1)的對(duì)數(shù)的圖像恒過點(diǎn)P,P的坐標(biāo)?
4.若函數(shù)y=以a為底[ax²+(a-1)x+四分之一]的對(duì)數(shù)的定義域?yàn)镽,求a的范圍?
5.設(shè)a大于1,函數(shù)f(x)=以a為底x的對(duì)數(shù)在區(qū)間[a,2a]上的最大值與最小值之差為0.5,a=?
1)恒過定點(diǎn)(3,0)
2)由條件可得關(guān)系式:4-x》0;x-1+根號(hào)4-x>0解得(1-根號(hào)10)/2
3)恒過定點(diǎn)(2,0)
4)由條件可得ax^2+(a-1)x+1/4>0在定義域R上恒成立,當(dāng)a=0時(shí)很顯然 不滿足條件故a不等于0
設(shè)f(x)=ax^2+(a-1)x+1/4易知若使不等式成立,則使函數(shù)圖象在x軸上方即可,此時(shí)有a>0;delta=(a-1)^2-a<0解得、0
5)由條件易知對(duì)數(shù)函數(shù)單調(diào)遞增則最大值為loga2a=1+loga2,最小值為logaa=1又知兩值之差為0.5則有l(wèi)oga2=0.5推得a=4