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 20 - 2018 - Paper 1
Question 20
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)
Worked Solution & Example Answer: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 20 - 2018 - Paper 1
Show that $g(f(x)) = 2x(x + 2)$
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To show that g(f(x))=2x(x+2), we start by calculating f(x):
-
Calculate f(x):
f(x) &= (x + 1)^2 \
&= x^2 + 2x + 1
\\
ext{Next, we substitute } f(x) ext{ into } g(x):
\\
g(f(x)) = g(x^2 + 2x + 1) = 2((x^2 + 2x + 1) - 1)
\\
= 2(x^2 + 2x) = 2x(x + 2)
\\
ext{Thus, we have shown that } g(f(x)) = 2x(x + 2).
\
ext{This confirms the required result.}
\
ext{Hence, } g(f(x)) = 2x(x + 2).
\
\
Find $g(7)$
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To find g(7), we will use the function definition g(x)=2(x−1):
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Substitute x=7 into g(x):
g(7) &= 2(7 - 1) \
&= 2 imes 6 \
&= 12
\
ext{Thus, } g(7) = 12.
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