For all values of $x$ $f(x) = (x + 1)^2$ and $g(x) = 2(x - 1)$ (a) Show that $g(f(x)) = 2x(x + 2)$ (b) Find $g(7)$ (Total for Question 19 is 4 marks) - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2

To find $g(f(x))$, we first need to substitute $f(x)$ into the function $g(x)$.

1. Start with $f(x) = (x + 1)^2$. This can be expanded to:

   $f(x) = x^2 + 2x + 1$.

2. Now, substitute $f(x)$ into $g(x)$, where $g(x) = 2(x - 1)$:

   $g(f(x)) = 2((x + 1)^2 - 1)$

   This becomes:

   $g(f(x)) = 2(x^2 + 2x + 1 - 1)$

   Simplifying further, we get:

   $g(f(x)) = 2(x^2 + 2x)$

   Finally, this simplifies to:

   $g(f(x)) = 2x(x + 2)$

   Thus, we have shown that $g(f(x)) = 2x(x + 2)$.