How Is the Value of k Determined in These Function Compositions?

[nokia8650]

The functions f and g are defined by:

f(x) = x^2 - 2x +3

g(x) = k(x^2) + 1

Given that gf(2) = 16, find the value of k

My solution:

f(2) = 3

g(3) = 9k +1

9k + 1 = 16

k = 15/9

However, the markscheme quotes "16=3k+1" therefore k =5.

I am unable to understand how the markscheme came to this conclusion, please can someonebody help with this. The markscheme may have a mistake, which is what I am thinking!

Thanks

 

[exk]

Your solution looks fine to me. Looks like the key may have made a mistake of not squaring the 3 or something.

 

[Defennder]

Yeah, it looks like the answer key didn't take into account the square.