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Here are two functions - OCR - GCSE Maths - Question 11 - 2018 - Paper 4
Question 11
Here are two functions. Function A : input × 2 Function A : input − 1 Composite function C is shown below. Function C : input Function A output Function B out... show full transcript
Worked Solution & Example Answer:Here are two functions - OCR - GCSE Maths - Question 11 - 2018 - Paper 4
Step 1
(a) The output from function C is 54. Work out the input.
Answer
To find the input for function C, we first analyze its structure. The output of function C is the output of function B, which takes the output from function A.
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Let the input to function C be denoted as ( y ).
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The output from Function A is calculated as follows:
- Applying Function A: ( A(y) = 2y - 1 )
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Next, we compute the output of Function B based on the output from Function A:
- Applying Function B: ( B(A(y)) = 3(2y - 1) )
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Setting the output of Function C equal to 54:
[ B(A(y)) = 3(2y - 1) = 54 ]
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Expanding and solving for ( y ):
- [ 6y - 3 = 54 ]
- [ 6y = 57 ]
- [ y = \frac{57}{6} = 9.5 ]
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Therefore, the input to function C is 9.5.
Step 2
(b) The input to function C is x. Find an expression, in terms of x, for the output from function C.
Answer
To find the expression for the output from function C in terms of ( x ):
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Substitute ( x ) into Function A:
- [ A(x) = 2x - 1 ]
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Next, we substitute this output into Function B:
- [ B(A(x)) = 3(2x - 1) ]
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Simplifying gives:
- [ B(A(x)) = 6x - 3 ]
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Therefore, the output from function C, in terms of ( x ), is:
[ C(x) = 6x - 3 ]