Grade 7 Inverse Functions Interpret the reverse process

Lesson Plan Lesson Overview Objective(s) Interpret the reverse process as an inverse function, including

What is an inverse function? A function is like a number machine, you have

Take Notes: Notation f(x)= means ’function of x’ you may have seen it written

Practice Find the inverse function for the following:

Answers Find the inverse function for the following:

Reasoning • You can’t take the square root of a negative number (try it)

Inverse Function Notation f(x) = f -1(x) = f(x)= 8 x-4. Find the inverse

Practice Find the inverse function for the following: When working with inverses, there are

Exam Question – Specimen Papers 1 mark 2 marks 3 marks Student Sheet 3

Slides: 17

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Grade 7 Inverse Functions Interpret the reverse process as an inverse function, including the correct notation. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Lesson Plan Lesson Overview Objective(s) Interpret the reverse process as an inverse function, including the correct notation Grade Prior Knowledge Composite functions Rearranging equations. Inverse operations Duration Suggestion for this lesson to follow that on composite functions. 35 minutes for inverse functions (and exam practice) Resources Print slides: 15 - 17 7 Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) What is an inverse function Give students slide 15 printed. 5 Using slide 4 and 5 show students how an inverse function is formed, with particular attention to the ordering within the rearrangement. How to form the inverse of a function Using slide 6 and 7 demonstrate with 2 examples how to rearrange a function to find the inverse form. 15 Give students slide 16. Students to practice by completing the 10 practice questions. Solutions on slide 9. Further reasoning question on slide 10 for students to consider before discussing the solution. Composite and inverse functions in exam questions (from specimen papers) Give students slide 17. This includes 4 exam questions related to objective (and composite functions). Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show the marks are allocated. Next Steps Assessment PLC/Reformed Specification/Target 7/Algebra/Inverse Functions 15

Key Vocabulary Inverse Reverse Notation

What is an inverse function? A function is like a number machine, you have an input, some operations and an output. When you find an inverse function, you go through the number machine backwards. It could be simple: Find the inverse of the function: Or more complicated If f(x)=8 x-4, find f-1(x) So you need to understand the notation.

Take Notes: Notation f(x)= means ’function of x’ you may have seen it written as y= before now f -1(x)= means ‘inverse function of x’, or going through the function machine backwards.

Example 1

Example 2

Practice Find the inverse function for the following:

Answers Find the inverse function for the following:

Reasoning • You can’t take the square root of a negative number (try it) so the number under the square root must be positive. This means that x-5≥ 0 so if x<5, it won’t work.

Exam Question – Specimen Papers

Inverse Function Notation f(x) = f -1(x) = f(x)= 8 x-4. Find the inverse function of x. Student Sheet 1

Practice Find the inverse function for the following: When working with inverses, there are some values that won’t work in inverse functions. f -1 (x)=, is an example where certain values for x won’t work. What are the numbers that will not work and why? Student Sheet 2

Exam Question – Specimen Papers 1 mark 2 marks 3 marks Student Sheet 3 2 marks 3 marks