Here are two functions. Function A: Input + 5 Function B: Input x 2 - 1 (a) Write an algebraic expression for the output of function A when the input is x. (b) Here is a composite function C. Function C: Input The input to function C is x. The output from function C is 2x + 1. Find the value of x. You must show your working.

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Here are two functions - OCR - GCSE Maths - Question 12 - 2023 - Paper 4

Question 12

Here are two functions. Function A: Input + 5 Function B: Input x 2 - 1 (a) Write an algebraic expression for the output of function A when the ... show full transcript

Worked Solution & Example Answer:Here are two functions - OCR - GCSE Maths - Question 12 - 2023 - Paper 4

Step 1

Write an algebraic expression for the output of function A when the input is x.

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Answer

To find the output of function A, we start with the input, which is represented by x. The function A performs the following operations on this input:

Add 5 to x:

Output after first operation: $x + 5$
Multiply the result by 3:

Final output for function A can be expressed as:

$3(x + 5)$

Thus, the algebraic expression for the output of function A is:

$3(x + 5)$

Step 2

Find the value of x.

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Answer

We are given that the output from function C is $2x + 1$ . Knowing that the output from function C is also dependent on function A, we can equate this to the output of function A when the input is x:

Set the equation:

$3(x + 5) = 2x + 1$
Expand the left side of the equation:

$3x + 15 = 2x + 1$
Rearranging the equation gives:

$3x - 2x = 1 - 15$

$x = -14$

Thus, the value of x is -14.

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