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Define a function f:R→Rf : \mathbb{R} \to \mathbb{R}f:R→R such that f(f(x))=x2−x+1f(f(x))=x^2-x+1f(f(x))=x2−x+1 for all real xxx.
Evaluate f(0)= ? f(0) = \, \text{? } f(0)=? .
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If f(x2015+1)=x4030+x2015+1f(x^{2015}+1)=x^{4030}+x^{2015}+1f(x2015+1)=x4030+x2015+1, then what is sum of the coefficients of f(x2015−1)?f(x^{2015}-1)?f(x2015−1)?
f(x) f(1x)=f(x)+f(1x)\large f(x) \ f\left(\dfrac 1 x\right) = f(x) + f\left(\dfrac 1 x\right)f(x) f(x1)=f(x)+f(x1)
A polynomial fff satisfies the above equation and f(10)=1001.f(10) = 1001.f(10)=1001. Find the value of f(20).f(20).f(20).
f(x)=9x9x+3\large f(x)=\frac{9^x}{9^x+3}f(x)=9x+39x
Suppose we define f(x)f(x) f(x) as above. Let a=f(x)+f(1−x)a=f(x)+f(1-x) a=f(x)+f(1−x) and b=f(11996)+f(21996)+f(31996)+…+f(19951996).b=f\left(\frac1{1996}\right) + f\left(\frac2{1996}\right) + f\left(\frac3{1996}\right)+\ldots+ f\left(\frac{1995}{1996}\right).b=f(19961)+f(19962)+f(19963)+…+f(19961995).
Evaluate a+ba + ba+b.
If f(x)=ax+bf\left( x \right) =ax+bf(x)=ax+b, where aaa and bbb are real numbers, and f(f(f(x)))=8x+21f\left( f\left( f\left( x \right) \right) \right) =8x+21f(f(f(x)))=8x+21, what is a+ba+ba+b?
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