Question

if f(x)=2x-1/5x-2 verify whether (fof)(x)=x.

x does not belongs to 2/5

Answer 1

Answer:

Yes,it is verified that fof(x)=x

Step-by-step explanation:

To verify

$fof(x) = x \\ \\ if \\ \\ f(x) = \frac{2x - 1}{5x - 2} \: \: \: \: x \neq \frac{2}{5} \\ \\ \\ fof(x) = \frac{2\big(\frac{2x - 1}{5x - 2}\big) - 1}{5\big(\frac{2x - 1}{5x - 2}\big) - 2} \\ \\ fof(x) = \frac{\big(\frac{4x - 2 - 5x + 2}{5x - 2}\big) }{\big(\frac{10x - 5 - 10x + 4}{5x - 2}\big) } \\ \\ \\ fof(x) = \frac{4x - 5x - 2 + 2}{10x - 10x - 5 + 4} \\ \\ fof(x) = \frac{ - x}{ - 1} \\ \\ fof(x) = x$

Hence proved.

Answer 2

Answer:

(x) = [2x – 1] / [x + 5] = y

xy + 5y = 2x – 1

xy – 2x = – 1 – 5y

x = [- 1 – 5y] / [y – 2]

y = [- 1 – 5x] / [x – 2]

= [5x + 1] / [2 – x], x ≠ 2