Find the inverse of the function: x → 6 - 5 x

A function can be represented by a function machine. The function machine for x → 6 - 5 x is: x → × ( - 5 ) → - 5 x + 6 → 6 - 5 x The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations(BIDMAS) in reverse. 6 - x 5 ← ÷ 5 ← x - 6 - 6 ← x So, the inverse of the function is 6 - x 5 .

Find the inverse of the function: x → x + 4 3

A function can be represented by a function machine. The function machine for x → x + 4 3 is: x → + 4 → x + 4 ÷ 3 → x + 4 3 The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations(BIDMAS) in reverse. 3 x - 4 ← - 4 ← 3 x × 3 ← x So, the inverse of the function is 3 x - 4 .

Find the inverse of the function: x → x - 8 5

A function can be represented by a function machine. The function machine for x → x - 8 5 is: x → - 8 → x - 8 ÷ 5 → x - 8 5 The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations (BODMAS) in reverse. 5 x + 8 ← + 8 ← 5 x × 5 ← x So, the inverse of the function is 5 x + 8 .

Find the inverse of the function: x → 2 ( x - 3 )

A function can be represented by a function machine. The function machine for x → 2 ( x - 3 ) is: x → - 3 → x - 3 × 2 → 2 ( x - 3 ) The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations (BODMAS) in reverse. x 2 + 3 ← + 3 ← x 2 ÷ 2 ← x So, the inverse of the function is x 2 + 3 .

Find the inverse of the function: x → x 3 + 5

A function can be represented by a function machine. The function machine for x → x 3 + 5 is: x → ÷ 3 → x 3 + 5 → x 3 + 5 The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations(BODMAS) in reverse. 3 ( x - 5 ) ← × 3 ← x - 5 - 5 ← x So, the inverse of the function is 3 ( x - 5 ) .

Find the inverse of the function: x → x 2 - 7

A function can be represented by a function machine. The function machine for x → x 2 - 7 is: x → ÷ 2 → x 2 - 7 → x 2 - 7 The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations (BODMAS) in reverse. 2 ( x + 7 ) ← × 2 ← x + 7 + 7 ← x So, the inverse of the function is 2 ( x + 7 ) .

Find the inverse of the function: 1 2 x + 1

A function can be represented by a function machine. The function machine for x → 1 2 x + 1 is: x → + 1 → x + 1 ÷ 2 → x + 1 2 The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations(BODMAS) in reverse. 2 x - 1 ← - 1 ← 2 x × 2 ← x So, the inverse of the function is 2 x - 1 .

Sam says that the inverse function of x → 2 ( x - 1 ) is the same as the inverse of the function f ) x → 2 x - 2 . Is Sam correct? Explain your answer.

Let us first consider the function: x → 2 ( x - 1 ) A function can be represented by a function machine. The function machine for x → 2 ( x - 1 ) is: x → - 1 → x - 1 × 2 → 2 ( x - 1 ) The inverse function can be founded by reversing the function machine. When you are finding the inverse function, you must apply the order of operations(BODMAS) in reverse. x 2 + 1 ← + 1 ← x 2 ÷ 2 ← x So, the inverse function is x 2 + 1 . Now consider the function f ) x → 2 x - 2 A function can be represented by a function machine. The function machine for x → 2 x - 2 is: x → × 2 → 2 x - 2 → 2 x - 2 The inverse function can be founded by reversing the function machine. x 2 + 1 ← ÷ 2 ← x + 2 + 2 ← x So, the inverse function is x 2 + 1 . Thus, inverse of both functions is same. So, Sam is correct.

E M B I B E

Cambridge Lower Secondary Maths Stage 9: Student's Book>Algebra and Geometry>Chapter 18 - Linear Functions and Graphs>Exercise 1

Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 2: Exercise 1

Author:Michele Conway, Belle Cottingham, Alastair Duncombe & Amanda George

Michele Conway Mathematics Solutions for Exercise - Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 2: Exercise 1

Attempt the free practice questions from Exercise 2: Exercise 1 with hints and solutions to strengthen your understanding. Cambridge Lower Secondary Maths Stage 9: Student's Book solutions are prepared by Experienced Embibe Experts.

Questions from Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 2: Exercise 1 with Hints & Solutions

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 3

Find the inverse of the function: $x \to 6 - 5 x$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 4

Find the inverse of the function: $x \to \frac{x + 4}{3}$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 4

Find the inverse of the function: $x \to \frac{x - 8}{5}$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 4

Find the inverse of the function: $x \to 2 (x - 3)$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 4

Find the inverse of the function: $x \to \frac{x}{3} + 5$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 4

Find the inverse of the function: $x \to \frac{x}{2} - 7$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 4

Find the inverse of the function: $\frac{1}{2} (x + 1)$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 18 - Linear Functions and Graphs>Exercise 1>Q 5

Sam says that the inverse function of $x \to 2 (x - 1)$ is the same as the inverse of the function $f) x \to 2 x - 2$ . Is Sam correct? Explain your answer.

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