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Here is a function - OCR - GCSE Maths - Question 6 - 2023 - Paper 1

Question 6

Here is a function. Input ×4 +7 Output (a) Find the input when the output is 87. (b) The input is x and the output is y. Write an equation for y in terms of x.

Worked Solution & Example Answer:Here is a function - OCR - GCSE Maths - Question 6 - 2023 - Paper 1

Step 1

Find the input when the output is 87.

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Answer

To find the input when the output is 87, we start by setting up the function based on the representation provided. The output (y) can be expressed with the formula:

$y = 4x + 7$

We need to solve for x when y = 87:

$87 = 4x + 7$

Next, we isolate the variable x:

$87 - 7 = 4x$

This simplifies to:

$80 = 4x$

Now, divide both sides by 4:

$x = \frac{80}{4} = 20$

Thus, the input when the output is 87 is 20.

Step 2

Write an equation for y in terms of x.

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Answer

To write the equation for y in terms of x, we can start from the initial representation of the function:

$y = 4x + 7$

This is the required equation that shows how y depends on x.

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