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Here are two functions - OCR - GCSE Maths - Question 13 - 2019 - Paper 5

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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.

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Answer

To find the inverse of function A, we start with its expression:

y=3x−2y = 3x - 2

To find the inverse, we swap x and y:

x=3y−2x = 3y - 2

Next, we solve for y:

  1. Add 2 to both sides:
    x+2=3yx + 2 = 3y
  2. Divide by 3:
    y=x+23y = \frac{x + 2}{3}

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

Inverse of A=x+23\text{Inverse of A} = \frac{x + 2}{3}

Step 2

Find the value x when z = 4x.

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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.

  1. From the previous step, we have Function A's output as:
    y=3x−2y = 3x - 2
  2. Applying this in Function B, we can express z:
    z=(3x−2)+7z = (3x - 2) + 7
    z=3x+5z = 3x + 5

Setting this equal to 4x:
3x+5=4x3x + 5 = 4x

  1. Rearranging gives:
    5=4x−3x5 = 4x - 3x
    5=x5 = x

Thus, the value of x when z = 4x is:
x=5x = 5

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