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Here are two functions - OCR - GCSE Maths - Question 13 - 2019 - Paper 5
Question 13
Here are two functions. Function A $\qquad x \rightarrow x \times 3 - 2 \qquad y$ Function B $\qquad x \rightarrow x + 7 \qquad y$ (a) Find an algebraic express... show full transcript
Worked Solution & Example Answer:Here are two functions - OCR - GCSE Maths - Question 13 - 2019 - Paper 5
Step 1
Find an algebraic expression for the output of the inverse of function A when the input is x.
Answer
To find the inverse of function A, we start with its expression:
To find the inverse, we swap x and y:
Next, we solve for y:
- Add 2 to both sides:
- Divide by 3:
Thus, the algebraic expression for the output of the inverse of function A is:
Step 2
Find the value x when z = 4x.
Answer
To find the value of x when z = 4x, we need to first express z in terms of x using the composite function C, which consists of Function A and Function B.
- From the previous step, we have Function A's output as:
- Applying this in Function B, we can express z:
Setting this equal to 4x:
- Rearranging gives:
Thus, the value of x when z = 4x is: