Question

Let f be a function such that f(f(x)) = f(x + 13) 18 for all integers x. If f (241) = 259 and f(259) = 254, then f(267) is?

Answer 1

Answer:

The answer is 308.

Step-by-step explanation:

We are given:

f(f(x) = f(x+13)-18

and  

f(241) = 259

f(259) = 254

We need to find f(267):

First we put x = 241.

f(f(241))= f(241+13)-18

f(259)=f(254)-18

254+18=f(254)  

272=f(254)----------(1)

Similarly,  

we'll put x = 259.  

f(f(259))=f(259+13)-18

f(254)=f(272)-18

Using eqation (1), we get

272+18=f(272)  

290=f(272)------------(2)

Now, we'll put x = 254.

f(f(254))=f(254+13)-18

f(272)=f(267)-18

Using equation (2), we get

290=f(267)-18

290+18=f(267)

308=f(267)

Hence, the value of f(267) = 308.

Answer 2

Answer:

308

Step-by-step explanation:

f(241) = 259 (Given) ---1

f(259) = 254 (Given) --- 1

Let f be the function such that f(f(x)) = f(x + 13) - 18

Putting x = 241  

= ff(241)  = f(241 + 13) - 18  

f(259) = f(254) - 18 ( eq 1)

254 + 18 = f(254) ( eq 2)

f(254) = 272 ---3

Putting x = 259  

= ff(259) = f(259 + 13) - 18

= f(254) = f(272) - 18 ( eq 2)

= 272 + 18 = f(272) ( eq 3)

= f(272) = 290  

Putting x = 254.

ff(254) = f(254+13)-18

f(272)=f(267)-18

Using equation (2), we will get -

290 = f(267)-18

290+18 = f(267)

308 = f(267)

Therefore, the value of f(267) = 308.