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# New Gcse Maths Hard question

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1. I'm struggling answering a question about function notation in the new Gcse papers. Here is the question:

f(x)=2x+c
g(x)=cx+5
fg(x)=6x+d
c and d are constants
workout the value of d

any help will be appreciated
2. (Original post by theBranicAc)
I'm struggling answering a question about function notation in the new Gcse papers. Here is the question:

f(x)=2x+c
g(x)=cx+5
fg(x)=6x+d
c and d are constants
workout the value of d

any help will be appreciated
Zacken can help.
3. (Original post by theBranicAc)
I'm struggling answering a question about function notation in the new Gcse papers. Here is the question:

f(x)=2x+c
g(x)=cx+5
fg(x)=6x+d
c and d are constants
workout the value of d

any help will be appreciated
What is f(g(x))? It is

But we know that so it must be the case that

And hence: and . You can find the value of c from the first equation and hence the value of d from the second.
4. (Original post by TheOtherSide.)
Zacken can help.
Thanks.
5. (Original post by Zacken)
What is f(g(x))? It is

But we know that so it must be the case that

And hence: and . You can find the value of c from the first equation and hence the value of d from the second.
I understand everything up onto the 2c = 6 part. How did you go from 2cx + 10 + c = 6x + d to 2c = 6?

And also solving c, you get c = 3 therefore d = 13.
6. What exam board are you taking?
7. (Original post by theBranicAc)
I understand everything up onto the 2c = 6 part. How did you go from 2cx + 10 + c = 6x + d to 2c = 6?

And also solving c, you get c = 3 therefore d = 13.
You compared the coefficients of x on both sides of the equation. They need to be equal for the equality to hold.
8. (Original post by Zacken)
You compared the coefficients of x on both sides of the equation. They need to be equal for the equality to hold.
I'm sorry but I still do not understand? I can see the coefficients of x are 2 and 6 but how does that lead to 2c = 6?
9. (Original post by theBranicAc)
I understand everything up onto the 2c = 6 part. How did you go from 2cx + 10 + c = 6x + d to 2c = 6?

And also solving c, you get c = 3 therefore d = 13.
For the left hand side to be exactly the same as the right hand side, 2c must be equal to 6, as the coefficients of the x term must be same on both sides of equation.

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