Let f:R→R be a function defined by f(x)=4x4x+2 what is the value of f(14)+2f(12)+f(34)=

f(x)=4x4x+2 f(x)+f(1−x)=4x4x+2+41−x41−x+2 =4x4x+2+24x+2=1 f(14)+2f(12)+f(34) =f(14)+f(1−14)+2×f(12) =1+2(22+2)=2

Let f:R→R be a function defined by f(x)=4x4x+2 what is the value of f(14)+2f(12)+f(34)=

f(x)=4x4x+2 f(x)+f(1−x)=4x4x+2+41−x41−x+2 =4x4x+2+24x+2=1 f(14)+2f(12)+f(34) =f(14)+f(1−14)+2×f(12) =1+2(22+2)=2

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Let $f : R \to R$ be a function defined by $f (x) = \frac{4^{x}}{4^{x} + 2}$ what is the value of $f (\frac{1}{4}) + 2 f (\frac{1}{2}) + f (\frac{3}{4}) =$

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Detailed Solution

$f (x) = \frac{4^{x}}{4^{x} + 2} f (x) + f (1 - x) = \frac{4^{x}}{4^{x} + 2} + \frac{4^{1 - x}}{4^{1 - x} + 2} = \frac{4^{x}}{4^{x} + 2} + \frac{2}{4^{x} + 2} = 1 f (\frac{1}{4}) + 2 f (\frac{1}{2}) + f (\frac{3}{4}) = f (\frac{1}{4}) + f (1 - \frac{1}{4}) + 2 \times f (\frac{1}{2}) = 1 + 2 (\frac{2}{2 + 2}) = 2$