## 2015 regional Secondary no. 6 function algebra

For discussing Olympiad Level Algebra (and Inequality) problems
Md. Rifat uddin
Posts: 10
Joined: Thu Dec 15, 2016 1:32 pm

### 2015 regional Secondary no. 6 function algebra

Plz solve this problem...... Thanks in advance.....
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asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### Re: 2015 regional Secondary no. 6 function algebra

Hint

mdhasib
Posts: 10
Joined: Fri Jul 22, 2016 11:43 am

### Re: 2015 regional Secondary no. 6 function algebra

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

asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### Re: 2015 regional Secondary no. 6 function algebra

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().

mdhasib
Posts: 10
Joined: Fri Jul 22, 2016 11:43 am

### Re: 2015 regional Secondary no. 6 function algebra

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 .