Question

求高一数学函数解答

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Answer 1

f(x)=4^x/(4^x+2)
1.f(a)+f(1-a)
=4^a/(4^a+2)+4^[1-a]/(4^[1-a]+2) (分子分母同时乘以4^a)
=4^a/(4^a+2)+4/(4+2*4^a)
=4^a/(4^a+2)+2/(2+4^a)
=(4^a+2)/(4^a+2)
=1
2. 由(1)可知f(a)+f(1-a)=1
即f(1/100)+f(99/100)=f(1/100)+f(1-1/宽模100)=1
f(2/脊巧陵100)+f(98/100)=1
……
f(99/100)+f(1/100)=1
f(1/100)+f(2/100)+……+f(98/100)+f(99/100)
=[f(1/100)+f(99/100)]+[f(2/100)+f(98/100)]+…樱戚…+[f(49/100)+f(51/100)]+f(50/100)
=49+f(1/2)
=49+1/2
=49.5