函数f(x)=cx/2x+3(x≠-2/3)满足f〔f(x)〕=x,则c等于( )A.3 B.-3 C.3或-3 D.5或-3
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![函数f(x)=cx/2x+3(x≠-2/3)满足f〔f(x)〕=x,则c等于( )A.3 B.-3 C.3或-3 D.5或-3](/uploads/image/z/7625081-65-1.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3Dcx%2F2x%2B3%28x%E2%89%A0-2%2F3%29%E6%BB%A1%E8%B6%B3f%E3%80%94f%28x%29%E3%80%95%3Dx%2C%E5%88%99c%E7%AD%89%E4%BA%8E%EF%BC%88+%EF%BC%89A.3+B.-3+C.3%E6%88%96-3+D.5%E6%88%96-3)
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函数f(x)=cx/2x+3(x≠-2/3)满足f〔f(x)〕=x,则c等于( )A.3 B.-3 C.3或-3 D.5或-3
函数f(x)=cx/2x+3(x≠-2/3)满足f〔f(x)〕=x,则c等于( )
A.3 B.-3 C.3或-3 D.5或-3
函数f(x)=cx/2x+3(x≠-2/3)满足f〔f(x)〕=x,则c等于( )A.3 B.-3 C.3或-3 D.5或-3
A.3
要用待定系数法
f[f(x)]=x,直接将f(x)=cx/(2x+3)代入到x中
化简得到:(c^2 *x)/[(2c+6)x+9x]=x
最后化简得到:c^2 *x=(2c+6)x^2+9x 要恒成立
则 c^2=9 (一次项系数要相同,二次项系数要相同)
2c+6=0 两式联立解得c=-3