GCSE OCR Maths Cumulative frequency/box plots: Here is a function. Function A:

Here is a function - OCR - GCSE Maths - Question 17 - 2018 - Paper 1

Question 17

Here is a function. Function A: Input → + 14 → x 5 → Output. (a) The output of function A is x. Write an algebraic expression, in terms of x, for the input of fun... show full transcript

Worked Solution & Example Answer:Here is a function - OCR - GCSE Maths - Question 17 - 2018 - Paper 1

Step 1

Write an algebraic expression, in terms of x, for the input of function A.

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Answer

To find the input of function A in terms of the output x, we can reverse the operations applied in the function. The output x is produced by first multiplying the input by 5 and then adding 14. Therefore, we can express the input as follows:

Start with the output: $x = 5 imes \text{Input} + 14$
Rearrange the equation to isolate the input: $x - 14 = 5 \times \text{Input}$ $\text{Input} = \frac{x - 14}{5}$

Thus, the algebraic expression for the input of function A is:
$\text{Input} = \frac{x - 14}{5}$

Step 2

Find the value of k.

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Answer

Given that the output is also k, we can substitute k for the output in the expression derived in part (a):

Set the original equation equal to k: $k = 5 \times \text{Input} + 14$
We also know that the input is k, so: $k = 5k + 14$
Rearranging this gives: $k - 5k = 14$ $-4k = 14$ $k = -\frac{14}{4}$ $k = -\frac{7}{2}$

Thus, the value of k is:
$k = -3.5$

Here is a function - OCR - GCSE Maths - Question 17 - 2018 - Paper 1

Worked Solution & Example Answer:Here is a function - OCR - GCSE Maths - Question 17 - 2018 - Paper 1

Write an algebraic expression, in terms of x, for the input of function A.

Find the value of k.

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