If f (x) = \(\frac{4^x}{4^x+2}\) , then f (x) + f (1 – x) is equa

1.	If f (x) = \(\frac{4^x}{4^x+2}\) , then f (x) + f (1 – x) is equal to (a) – 1 (b) 0 (c) 1 (d) None of these
Answer» Answer: (c) = 1 Given, f (x) = \(\frac{4^x}{4^x+2}\) f (1 – x) = \(\frac{4^{1-x}}{4^{1-x}+2}\) = \(\frac{4.4^{-x}}{4^1.4^{-x}+2}\) = \(\frac{4.\frac{1}{4^x}}{4.\frac{1}{4^x}+2}\) = \(\frac{\frac{4}{4^x}}{\frac{4+2.4^x}{4^x}}\) = \(\frac{4}{4+2.4^x}=\frac{2}{2+4^x}\) Now f (x) + f (1 – x) = \(\frac{4^x}{4^x+2}\) + \(\frac{2}{2+4^x}\) = \(\frac{4^x+2}{4^x+2}\) = 1

If f (x) = \(\frac{4^x}{4^x+2}\) , then f (x) + f (1 – x) is equal to (a) – 1 (b) 0 (c) 1 (d) None of these

Answer»

Answer: (c) = 1

Given,

f (x) = \(\frac{4^x}{4^x+2}\)

f (1 – x) = \(\frac{4^{1-x}}{4^{1-x}+2}\) = \(\frac{4.4^{-x}}{4^1.4^{-x}+2}\)

= \(\frac{4.\frac{1}{4^x}}{4.\frac{1}{4^x}+2}\)

= \(\frac{\frac{4}{4^x}}{\frac{4+2.4^x}{4^x}}\) = \(\frac{4}{4+2.4^x}=\frac{2}{2+4^x}\)

Now f (x) + f (1 – x) = \(\frac{4^x}{4^x+2}\) + \(\frac{2}{2+4^x}\)

= \(\frac{4^x+2}{4^x+2}\)

= 1