f(x)=x^2,g(x)=-1/2x+5,g^-1(x)表示g(x)的反函数,设F(x)=F(x)=f[g^-1(x)]-g^-1[f(x)],F(x)最小值为多少?
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![f(x)=x^2,g(x)=-1/2x+5,g^-1(x)表示g(x)的反函数,设F(x)=F(x)=f[g^-1(x)]-g^-1[f(x)],F(x)最小值为多少?](/uploads/image/z/5239182-30-2.jpg?t=f%28x%29%3Dx%5E2%2Cg%28x%29%3D-1%2F2x%2B5%2Cg%5E-1%28x%29%E8%A1%A8%E7%A4%BAg%28x%29%E7%9A%84%E5%8F%8D%E5%87%BD%E6%95%B0%2C%E8%AE%BEF%28x%29%3DF%28x%29%3Df%5Bg%5E-1%28x%29%5D-g%5E-1%5Bf%28x%29%5D%2CF%EF%BC%88x%EF%BC%89%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91%3F)
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f(x)=x^2,g(x)=-1/2x+5,g^-1(x)表示g(x)的反函数,设F(x)=F(x)=f[g^-1(x)]-g^-1[f(x)],F(x)最小值为多少?
f(x)=x^2,g(x)=-1/2x+5,g^-1(x)表示g(x)的反函数,设F(x)=
F(x)=f[g^-1(x)]-g^-1[f(x)],F(x)最小值为多少?
f(x)=x^2,g(x)=-1/2x+5,g^-1(x)表示g(x)的反函数,设F(x)=F(x)=f[g^-1(x)]-g^-1[f(x)],F(x)最小值为多少?
f(x)=x²,g(x)=-(1/2)x+5,g⁻¹(x)表示g(x)的反函数,设F(x)=f[g⁻¹(x)]-g⁻¹[f(x)],F(x)最小值为多少?
由g(x)=-(1/2)x+5得x=10-2g(x),故g⁻¹(x)=10-2x;
于是得F(x)=(10-2x)²-(10-2x²)=100-40x+4x²-10+2x²=6x²-40x+90=6[x²-(20/3)x]+90
=6[(x-10/3)²-100/9]+90=6(x-10/3)²-200/3+90=6(x-10/3)²+70/3≧70/3
即F(x)的最小值为70/3,此时x=10/3.
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