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画函数的图象、求函数的极值、判断函数的奇偶性、确定函数的单调区间等,一般都要以解析式y=f(x)为基础。因之,求出f(x)是必要的。下面介绍几种求法。一待定系数法例1.已知:f(x)为有理整函数且 f(2x)+f(3x+1)=13x~2+6x-1 求:f(x) 解:设f(x)=ax~2+bx+c 则f(2x)+f(3x+1) =13ax~2+(6a+5b)x+a+b+2c ∵ 13ax~2+(6a+5b)x+(a+b+2c) =13x~2+6x-1比较系数得则f(x)=x~2-1。二换元法例2若:f[f(x)]=(x+1)/(x+2)求:f(x)
Draw the function image, find the extremum of the function, determine the parity of the function, determine the monotonic interval of the function, and so on, generally based on the analytical formula y=f(x). Therefore, it is necessary to find f(x). The following introduces several methods. A undetermined coefficient example 1. Known: f (x) is a rational whole function and f (2x) + f (3x + 1) = 13x ~ 2 + 6x-1 Solution: f (x) Solution: Let f (x) =ax~2+bx+c Then f(2x)+f(3x+1) =13ax~2+(6a+5b)x+a+b+2c ∵ 13ax~2+(6a+5b)x+(a +b+2c) =13x~2+6x-1 The comparison coefficient is f(x)=x~2-1. Two-member law example 2 If: f[f(x)]=(x+1)/(x+2) Find: f(x)