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11. 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) (Total for Question 11 is 3 marks) - Edexcel - GCSE Maths - Question 12 - 2018 - Paper 2

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Question 12

11.-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)--------(Total-for-Question-11-is-3-marks)-Edexcel-GCSE Maths-Question 12-2018-Paper 2.png

11. 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) (Total for Question 11 is 3 marks)

Worked Solution & Example Answer:11. 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) (Total for Question 11 is 3 marks) - 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:

f(−5)=2(−5)2f(-5) = \frac{2}{(-5)^2}

Calculating this gives:

f(−5)=225f(-5) = \frac{2}{25}

Thus, the answer is (\frac{2}{25}).

Step 2

Find fg(1)

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Answer

First, we need to evaluate g(1):

g(1)=4(1)3=4g(1) = 4(1)^3 = 4

Next, we substitute this value into the function f:

f(g(1))=f(4)=242f(g(1)) = f(4) = \frac{2}{4^2}

Calculating this gives:

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

Thus, the answer is (\frac{1}{8}).

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