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高中数学必修 第一册(648题)






第205题



参考答案:\(\left[ {4,\frac{{17}}{2}} \right]\)



第207题



参考答案:\(\left[ {4, + \infty } \right)\)









第215题



参考答案:\( \left[\frac{\sqrt{2}}{2},\frac{\sqrt{6}}{2}\right]\cup \left[-\frac{\sqrt{6}}{2},-\frac{\sqrt{2}}{2}\right]\)


第216题


A.\(f\left ( {x} \right )=\frac {1} {1+x}\)

B.\(f\left ( {x} \right )=\frac {1+x} {x}\)

C.\(f\left ( {x} \right )=\frac {x} {1+x}\left ( {x≠0} \right )\)

D.\(f\left ( {x} \right )=x+1\)


参考答案:C


第217题


A.\(\frac {1} {x+2}\left ( {x≠-2} \right )\)

B.\(\frac {1+x} {x}\left ( {x≠0} \right )\)

C.\(\frac {1} {x}+2\left ( {x≠0} \right )\)

D.\(\frac {1} {x}-1\left ( {x≠0} \right )\)


参考答案:C


第218题


A.\(f\left ( {x} \right )=\frac {x} {1+{x}^{2}}\left ( {x≠-1} \right )\)

B.\(f\left ( {x} \right )=\frac {-2x} {1+{x}^{2}}\left ( {x≠-1} \right )\)

C.\(f\left ( {x} \right )=\frac {2x} {1+{x}^{2}}\left ( {x≠-1} \right )\)

D.\(f\left ( {x} \right )=\frac {-x} {1+{x}^{2}}\left ( {x≠-1} \right )\)


参考答案:C


第219题


A.\(f\left ( {x} \right )=x+\frac {1} {x}\)

B.\(f\left ( {x} \right )={x}^{2}+2\)

C.\(f\left ( {x} \right )={x}^{2}\)

D.\(f\left ( {x} \right )=\left ( {x-\frac {1} {x}} \right )^{2}\)


参考答案:B


第220题



参考答案:\(∵f(x)\)是二次函数,设\(f\left ( {x} \right )=a{x}^{2}+bx+c\mathrm{}(a\ne 0)\),由\(f(0)=1\),得\(c=1\),由\(f(x+1)-f(x)=2x\),

得\(a{(x+1)}^{2}+b(x+1)+1-a{x}^{2}-bx-1=2x\),

即\(2ax+(a+b)=2x\).

\( \therefore \left\{\begin{array}{c}2a=2\\ a+b=0\end{array}\right.\),\( \therefore \left\{\begin{array}{c}a=1\\ b=-1\end{array}\right.\),\(\therefore f\left ( {\mathrm{x}} \right )={x}^{2}-x+1\)


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