If f(x) = (5x + 3)/(4x-5), x is not equal to 5/4, show that fof is an identity function.

Question

hba · Answer

WELCOME TO OPEN STUDY

anonymous · Answer

thank yu

vishweshshrimali5 · Answer

:) Welcome @ashna

vishweshshrimali5 · Answer

Do you know what is the meaning of an identity function and fof.......

anonymous · Answer

$$
f(f(x))=\frac{\frac{5 (5 x+3)}{4
   x-5}+3}{\frac{4 (5 x+3)}{4 x-5}-5}
$$

vishweshshrimali5 · Answer

Now solve this................

anonymous · Answer

no i dont know .. @eliassaab should i solve that ? .. is the answer x ?

anonymous · Answer

$$
f(f(x))=\frac{\frac{5 (5 x+3)}{4
   x-5}+3}{\frac{4 (5 x+3)}{4 x-5}-5} =\frac{37 x}{\frac{37 (4 x-5)}{4 x-5}}=x
$$

vishweshshrimali5 · Answer

Identity function : a function which is true for all values of the variable.

and fof means function f of f(x)

anonymous · Answer

oh .. thanks :)

anonymous · Answer

Did you understand it?

vishweshshrimali5 · Answer

Now as u get the value x it means that the value of fof is a real value for any value of x except 5/4............

so fof becomes an identity function

anonymous · Answer

yes .. thank you .. can i ask another question ?

vishweshshrimali5 · Answer

@ashna 

Ask it as a seperate question

anonymous · Answer

okay !

hba · Answer

u would have to close this question to post another @ashna