Question

if f(x)=x^3-3x^2+1/x(x-1) show that f(1/x)=f(1-x)

Answer 1

Answer:

sometimes is wrong

f(1/x) ≠ f(1-x)

Step-by-step explanation:

$given \: \: \: \: \: f(x) = {x}^{3} - 3 {x}^{2} + \frac{1}{x(x - 1)} \\ now \\ lhs \: = \: f( \frac{1}{x} ) = { (\frac{1}{x} })^{3} - 3( { \frac{1}{x} })^{2} + \frac{1}{ \frac{1}{x} ( \frac{1}{x} - 1)} \\ = \frac{1}{ {x}^{3} } - \frac{3}{ {x}^{2} } + \frac{ {x}^{2} }{1 - x } \\ \\ rhs = f(1 - x) = (1 - x)^{3} - 3(1 - x)^{2} + \frac{1}{(1 - x)(1 - x - 1)} \\ = - {x}^{3} + 6x - 2 + \frac{1}{x(x - 1)} \\ so \: \: f( \frac{1}{x}) \: is \: not \: eqval \: to \: f(1 - x)$