f-2-x-f-x-2-2-f-2-x-stands-for-f-x-2-f-x-If-possible-solve-stepwise-

Question Number 1902 by Rasheed Soomro last updated on 23/Oct/15

f^{2} (x) - f (x^{2}) = 2, f^{2} (x) s t a n d s f o r {[f (x)]}^{2}

f (x) = ?

(I f p o s s i b l e s o l v e s t e p w i s e)

Commented by 123456 last updated on 23/Oct/15

hehe \dots sorry, i make a great confusion .

Commented by Rasheed Soomro last updated on 23/Oct/15

H o w y o u s u p p o s e d t h a t

f^{2} (0) = f (0^{2}) a n d f^{2} (1) = f (1^{2}) ?

Commented by 123456 last updated on 23/Oct/15

f^{2} (0) - f (0^{2}) = 2

f^{2} (0) - f (0) = 2

x = f (0)

x^{2} - x = 2

Δ = 1 + 8 = 9

x = \frac{1 \pm 3}{2}

x = - 1 \lor x = 2

f (0) = - 1 \lor f (0) = 2

by same way

f (1) = - 1 \lor f (1) = 2

Commented by Rasheed Soomro last updated on 24/Oct/15

G o o d T r y S i r! A c t u a l l y i f i t i s n e c e s s a r y t o m a k e c l e a r t h e n

r e a l l y x \neq 0 .

Answered by prakash jain last updated on 24/Oct/15

f (x) = a^{k \ln x} + a^{- k \ln x}

{[f (x)]}^{2} = a^{2 k \ln x} + a^{- 2 k \ln x} + 2

f (x^{2}) = a^{2 k \ln x} + a^{- 2 k \ln x}

{[f (x)]}^{2} - f (x^{2}) = 2

Commented by prakash jain last updated on 24/Oct/15

f (x) = x^{a} + x^{- a}

Commented by Rasheed Soomro last updated on 25/Oct/15

E x c e l l e n t S i r!