Bunuel wrote:

For which of the following functions does f(x) = f(1/x), given that x ≠ - 2, - 1, 0, or 1?

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

B. \(f(x) = |\frac{x+1}{x-1}|\)

C. \(f(x) = |\frac{x-1}{x}|\)

D. \(f(x) = |\frac{x}{x+1}|\)

E. \(f(x) = |\frac{x+1}{x+2}|\)

Kudos for a correct solution.

The CORRECT Option must satisfy the condition f(2) = f(1/2)So Checking Options:

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

i.e. \(f(2) = |\frac{2+1}{2}| = |\frac{3}{2}|\)

and \(f(1/2) = |\frac{0.5+1}{0.5}| = |\frac{3}{1}|\)

Since f(2) is NOT equal to f(1/2) Hence the INCORRECT OPTIONB. \(f(x) = |\frac{x+1}{x-1}|\)

i.e. \(f(2) = |\frac{2+1}{2-1}| = 3/1\)

and \(f(x) = |\frac{0.5+1}{0.5-1}| = 3/1\)

Since f(2) is equal to f(1/2) Hence the CORRECT OPTIONC. \(f(x) = |\frac{x-1}{x}|\)

D. \(f(x) = |\frac{x}{x+1}|\)

E. \(f(x) = |\frac{x+1}{x+2}|\)

Answer: Option B
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