用解析法表示函数(1)已知二次函数f(X)满足f(2X+1)=4X-6X+5,求f(X) (2)已知函数f(X+1/X)=X+1/X,求f(X)
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用解析法表示函数(1)已知二次函数f(X)满足f(2X+1)=4X-6X+5,求f(X) (2)已知函数f(X+1/X)=X+1/X,求f(X)
用解析法表示函数
(1)已知二次函数f(X)满足f(2X+1)=4X-6X+5,求f(X) (2)已知函数f(X+1/X)=X+1/X,求f(X)
用解析法表示函数(1)已知二次函数f(X)满足f(2X+1)=4X-6X+5,求f(X) (2)已知函数f(X+1/X)=X+1/X,求f(X)
令2x+|=t,所以x=(t-|)/2,再将此式代入等式就可得f(t)方程,再将t写作x就行了;同理令x+1/x=t,所以f(t)=t^2-2,即f(x)=x^2-2
(1)已知二次函数f(X)满足f(2X+1)=4X-6X+5,求f(X) t = 2x +1 ==> x = (t -1) /2 f(2X+1)=4X-6X+5 ==> f(t) = 4* [(t-1)/2]^2 - 6 * (t-1)/2 +5 ==> f(t) = (t-1)^2 - 3(t-1) + 5 ==> f(t) = t^2 - 2t +1 - 3t + 3 +5 ==> f(t) ...
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(1)已知二次函数f(X)满足f(2X+1)=4X-6X+5,求f(X) t = 2x +1 ==> x = (t -1) /2 f(2X+1)=4X-6X+5 ==> f(t) = 4* [(t-1)/2]^2 - 6 * (t-1)/2 +5 ==> f(t) = (t-1)^2 - 3(t-1) + 5 ==> f(t) = t^2 - 2t +1 - 3t + 3 +5 ==> f(t) = t^2 - 5t + 9 f(x) = x^2 - 5x + 9 (2)已知函数f(X+1/X)=X+1/X,求f(X) f(x +1/x) = x^2 + 1/x^2 = (x + 1/x)^2 - 2 t = x +1/x f(t) = t^2 - 2 f(x) = x^2 - 2
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