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https://vle.mathswatch.co.uk/images/questions/question2241.png

 Feb 11, 2018
 #1
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+2

f(x)   =  3x + p

 

g (x)  =  px + 4

 

f (g(x))  =  6x + q

 

Note that

 

f(g(x)  =   3 [px + 4] + p   =   3px + 12 + p

 

And this equals  6x + q

 

So

 

3px  + 12 + p   =  6x +  q

 

Equating terms we have that

 

3px   =   6x 

 

12 + p  = q

 

In the first equation, it's obvious that p  must   =  2

 

So.....

 

12 + 2  = q  ⇒    14  =   q

 

So   { p, q }  =  { 2, 14 }

 

 

 

cool cool cool

 Feb 12, 2018

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