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New Gcse Maths Hard question

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
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. :yep:
Reply 2
Avatar for Zacken
Zacken
22
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 f(cx+5)=2(cx+5)+c=2cx+10+cf(cx + 5) = 2(cx+5) + c = 2cx + 10 + c

But we know that f(g(x))=6x+df(g(x)) = 6x + d so it must be the case that 2cx+10+c=6x+d2cx + 10 + c = 6x + d

And hence: 2c=62c = 6 and 10+c=d10 + c = d. You can find the value of c from the first equation and hence the value of d from the second.
Reply 3
Avatar for Zacken
Zacken
22
Original post by TheOtherSide.
@Zacken can help. :yep:


Thanks. :smile:
Reply 4
Avatar for theBranicAc
theBranicAc
OP
3
Original post by Zacken
What is f(g(x))? It is f(cx+5)=2(cx+5)+c=2cx+10+cf(cx + 5) = 2(cx+5) + c = 2cx + 10 + c

But we know that f(g(x))=6x+df(g(x)) = 6x + d so it must be the case that 2cx+10+c=6x+d2cx + 10 + c = 6x + d

And hence: 2c=62c = 6 and 10+c=d10 + c = d. 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.
Reply 5
Avatar for Chaseyyy
Chaseyyy
5
What exam board are you taking?
Reply 6
Avatar for Zacken
Zacken
22
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.
Reply 7
Avatar for theBranicAc
theBranicAc
OP
3
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?
(edited 7 years ago)
Reply 8
Avatar for B_9710
B_9710
18
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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