已知函数f(x)=2^x,g(x)=-x^2+2x+b(b∈R),记h(x)=f(x)-1/f(x)(1)对任意x∈[1,2],都存在x1,x2属于[1,2],使得f(x)≤f(x1),g(x)≤g(x2),若f(x1)=g(x2),求实数b的值;(2)若2^x ×h(2x)+mh(x)≥0对于一切x∈[1,2]恒成立,求实
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![已知函数f(x)=2^x,g(x)=-x^2+2x+b(b∈R),记h(x)=f(x)-1/f(x)(1)对任意x∈[1,2],都存在x1,x2属于[1,2],使得f(x)≤f(x1),g(x)≤g(x2),若f(x1)=g(x2),求实数b的值;(2)若2^x ×h(2x)+mh(x)≥0对于一切x∈[1,2]恒成立,求实](/uploads/image/z/1749507-51-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2%5Ex%2Cg%28x%29%3D-x%5E2%2B2x%2Bb%28b%E2%88%88R%29%2C%E8%AE%B0h%28x%29%3Df%28x%29-1%2Ff%28x%29%EF%BC%881%EF%BC%89%E5%AF%B9%E4%BB%BB%E6%84%8Fx%E2%88%88%5B1%2C2%5D%2C%E9%83%BD%E5%AD%98%E5%9C%A8x1%2Cx2%E5%B1%9E%E4%BA%8E%5B1%2C2%5D%2C%E4%BD%BF%E5%BE%97f%28x%29%E2%89%A4f%28x1%29%2Cg%28x%29%E2%89%A4g%28x2%29%2C%E8%8B%A5f%28x1%29%3Dg%28x2%29%2C%E6%B1%82%E5%AE%9E%E6%95%B0b%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A52%5Ex+%C3%97h%EF%BC%882x%29%2Bmh%28x%29%E2%89%A50%E5%AF%B9%E4%BA%8E%E4%B8%80%E5%88%87x%E2%88%88%5B1%2C2%5D%E6%81%92%E6%88%90%E7%AB%8B%2C%E6%B1%82%E5%AE%9E)
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