问题补充:
已知函数f(x)满足f(ab)=f(a)+f(b),且f(2)=p,f(3)=q,则f(72)等于——A p+q B 3p+2q C 2p+3q D p³+q³ 答案是什么不重要 我要解题过程或解题思路
答案:
f﹙72﹚=f﹙2×2×2×3×3﹚=f﹙2﹚+f﹙2﹚+f﹙2﹚+f﹙3﹚+f﹙3﹚=3p+2q
======以下答案可供参考======
供参考答案1:
72=2*2*2*3*3
f(72)=f(8)+f(9) f(9)=f(3)+f(6)
f(8)=f(2)+f(4) f(6)=f(3)+f(3)
f(4)=f(2)+f(2)
供参考答案2:
f(6)=f(2)+f(3)=p+q
f(36)=2f(6)=2(p+q)
f(72)=f(36)+f(2)=2(p+q)+p=3p+2q
供参考答案3:
f(72)=f(8)+f(9)=3p+2q
f(8)=f(2)+f(4)=f(2)+f(2)+f(2)=3p
f(9)=f(3)+f(3)=2q
供参考答案4:
f(36)=2f(6)=2(f(2)+f(3))=2p+2q
f(72)=f(2)+f(36)=3q+2p
供参考答案5:
f(72)=f(8*9)=f(8)+f(9)
f(8)=f(2*4)=f(2)+f(4)=f(2)+f(2)+f(2)=3p
f(9)=f(3)+f(3)=2q
所以f(72)=3p+2q
供参考答案6:
解,由已知条件可得
f(72)=f(8×9)=f(8)+f(9)
=[f(2)+f(4)]+[f(3)+f(3)]
=[f(2)+f(2)+f(2)]+[f(3)+f(3)]
=3p+2q
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