### 2015 regional Secondary no. 6 function algebra

Posted:

**Sat Jan 07, 2017 10:16 pm**Plz solve this problem...... Thanks in advance.....

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Posted: **Sat Jan 07, 2017 10:16 pm**

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

Posted: **Sun Jan 08, 2017 2:30 pm**

Posted: **Mon Jan 09, 2017 12:04 pm**

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**

Posted: **Mon Jan 09, 2017 2:23 pm**

$F(F(x))$ is not equal to $4x+3$. $F(F(x))=f(f(f(f(x))))$ from your definition of $F$.mdhasib wrote:SupposeF(x)=ax+b, thenF(F(x))=(a^2)x+ab+bif we compare4x+3with(a^2)x+ab+b

How do you deduce that? And which statement do you refer to.mdhasib wrote:then we will getF(x)=2x+1orF(x)=-2x-3. Considering the next statement we can be sure thatF(x)=2x+1.

You are supposed to fiind out $f(x)$, not $F(x)$.mdhasib wrote:HenceF(2015)=(2*2015)+1=4031

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($$).

Posted: **Wed Jan 11, 2017 4:52 pm**

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 .