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Here is a function - OCR - GCSE Maths - Question 6 - 2023 - Paper 1
Question 6
Here is a function. Input × 4 Output + 7 (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 o... show full transcript
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.
Answer
To find the input when the output is 87, we denote the input as ( x ). The function can be expressed as:
- Multiply the input by 4: ( 4x ).
- Then add 7: ( 4x + 7 ).
Setting this equal to the output:
[ 4x + 7 = 87 ]
Next, solve for ( x ):
[ 4x = 87 - 7 ] [ 4x = 80 ] [ x = \frac{80}{4} ] [ x = 20 ]
Thus, the input is 20.
Step 2
Write an equation for y in terms of x.
Answer
In this part, we define the input as ( x ) and the output as ( y ). According to the function:
- The function multiplies the input by 4, yielding ( 4x ).
- Then it adds 7, resulting in the output:
[ y = 4x + 7 ]
Therefore, the equation for ( y ) in terms of ( x ) is:
[ y = 4x + 7 ]