Question 1010711
problem is:


f(x) = {{{(1/x - 9x) / (1 + 3x)}}}


what is f(1/x)


you replace x with 1/x and the equation becomes:


f(x) = {{{(1/(1/x) - 9*1/x) / (1 + 3*(1/x))}}}


1/(1/x) = 1*x = x
9*1/x = 9/x
3*(1/x) = 3/x


equation becomes:


f(1/x) = {{{(x-9/x) / (1 + 3/x)}}}


multiply numerator and denominator of this equation by x to get:


f(1/x) = {{{(x^2-9) / (x + 3)}}}


x^2 - 9 = (x-3) * (x+3)


equation becomes:


f(1/x) = {{{((x+3)*(x-3)) / (x+3)}}}


the x+3 in the numerator and in the denominator cancel out and you are left with:


f(1/x) = (x-3)