Question

if f(x) = x - 9 then find f(x) - f(1/x)​

Answer 1

Step-by-step explanation:

f(x)=x-9

f(1/x)=

$\frac{1}{f(x)} \\ = \frac{1}{x - 9} \\ f(x) - f( \frac{1}{x} ) = \\ x - 9 - \frac{1}{ x - 9} \\ = \frac{ (x - 9)(x - 9) - 1}{ \: x - 9} \\ = \frac{ {(x - 9)}^{2} - 1}{x - 9} \\ = \frac{ {x}^{2} - 2 \times 9 \times x + {9}^{2} - 1}{x - 9} \\ = \frac{{x}^{2} - 18x + 81 - 1}{x - 9} \\ = \frac{ {x}^{2} - 18x + 80}{x - 9} \\ ={\frac{x{\cancel{(x-18)}}+80}{{\cancel{(x-9)}}}} \\ ={\frac{2x+80}{1}} \\ =2x+80 \\ =2(x+40)$

hence your answer is

${\boxed{2(x+40)}}$