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Plz solve this problem...... Thanks in advance.....

Hint

Suppose F(x)=ax+b , then F(F(x))=(a^2)x+ab+b if we compare 4x+3 with (a^2)x+ab+b then we will get F(x)=2x+1 or F(x)=-2x-3 Considering the next statement we can be sure that F(x)=2x+1 .Hence F(2015)=(2*2015)+1=4031

mdhasib wrote:Suppose F(x)=ax+b , then F(F(x))=(a^2)x+ab+b if we compare 4x+3 with (a^2)x+ab+b

$F(F(x))$ is not equal to $4x+3$. $F(F(x))=f(f(f(f(x))))$ from your definition of $F$.

mdhasib wrote:then we will get F(x)=2x+1 or F(x)=-2x-3. Considering the next statement we can be sure that F(x)=2x+1.

How do you deduce that? And which statement do you refer to.

mdhasib wrote:Hence F(2015)=(2*2015)+1=4031

You are supposed to fiind out $f(x)$, not $F(x)$.

Also try to write equations in $\LaTeX$. It's not that hard. Write all the maths at https://www.codecogs.com/latex/eqneditor.php, copy paste the code and enclose them by two dollar signs($$).

thank you for pointing out my mistakes asif vai though i can not edit it . But i was trying to mean f(x) by F(x) and i didnt think of it as a problem and by the next statement i meant f(5^k)=((5^k)*(2^(k-2)))+2^(k-3). I didnt mention it because it would look hideous .