Question

Drag the tiles to the correct boxes. Not all tiles will be used. Consider the following function: f(x) = -3/4x+9. Place the steps for finding f^-1(x) in the correct order.​

Answer 1

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Explanation:

Answer 2

The steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12