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f and g are functions such that f(x) = \frac{2}{x^2} and g(x) = 4x^3 (a) Find f(-5) (b) Find fg(1) - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 2

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Question 12

f-and-g-are-functions-such-that--f(x)-=-\frac{2}{x^2}-and-g(x)-=-4x^3--(a)-Find-f(-5)--(b)-Find-fg(1)-Edexcel-GCSE Maths-Question 12-2018-Paper 2.png

f and g are functions such that f(x) = \frac{2}{x^2} and g(x) = 4x^3 (a) Find f(-5) (b) Find fg(1)

Worked Solution & Example Answer:f and g are functions such that f(x) = \frac{2}{x^2} and g(x) = 4x^3 (a) Find f(-5) (b) Find fg(1) - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 2

Step 1

Find f(-5)

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Answer

To find f(-5), we substitute -5 into the function f(x):

f(−5)=2(−5)2f(-5) = \frac{2}{(-5)^2}

Calculating this, we have:

f(−5)=225f(-5) = \frac{2}{25}

Thus, the answer is:

f(−5)=225f(-5) = \frac{2}{25}

Step 2

Find fg(1)

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Answer

First, we need to find g(1):

g(1)=4(1)3=4â‹…1=4g(1) = 4(1)^3 = 4 \cdot 1 = 4

Now, we will substitute g(1) into f:

f(g(1))=f(4)=2(4)2f(g(1)) = f(4) = \frac{2}{(4)^2}

Calculating this, we get:

f(4)=216=18f(4) = \frac{2}{16} = \frac{1}{8}

Therefore, the answer is:

fg(1)=18fg(1) = \frac{1}{8}

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