Find f - 1 ( x ) for the linear function f ( x ) = 1 2 x + 4 . Give your answers in the form f - 1 ( x ) = m x + c

Given that: the linear function f ( x ) = 1 2 x + 4 . We have to find f - 1 x in the form f - 1 ( x ) = m x + c We have, f ( x ) = 1 2 x + 4 Replace f ( x ) with y . y = 1 2 x + 4 Interchange the variables. x = 1 2 y + 4 Solve for y . 2 x = y + 8 ⇒ y = 2 x - 8 Replace the y with f - 1 x to show the final answer. Hence, f - 1 ( x ) = 2 x - 8 .

Find f - 1 ( x ) for the linear function f x = - 1 6 x + 3 . Give your answers in the form f - 1 ( x ) = m x + c .

Given that: the linear function f x = - 1 6 x + 3 . We have to find f - 1 x in the form f - 1 ( x ) = m x + c We have, f x = - 1 6 x + 3 Replace f ( x ) with y . y = - 1 6 x + 3 Interchange the variables. x = - 1 6 y + 3 Solve for y . x = - 1 6 y + 3 ⇒ y = - 6 x + 18 Replace the y with f - 1 x to show the final answer. Hence, f - 1 ( x ) = - 6 x + 18

E M B I B E

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3G>Q 3

MEDIUM

Diploma

IMPORTANT

Earn 100

Sketch a graph of a linear function with range $\{6\}$ .

Important Questions on Modelling Relationships: Linear and Quadratic Functions

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3G>Q 4

Sketch a graph of a line that is not a function.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3G>Q 4

Find $f^{- 1} (x)$ for the linear function $f (x) = \frac{1}{2} x + 4$ . Give your answers in the form $f^{- 1} (x) = m x + c$

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3H>Q 1

Find $f^{- 1} (x)$ for the linear function $f (x) = - 3 x + 9$ . Give your answers in the form $f^{- 1} (x) = m x + c$

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3H>Q 1

Find $f^{- 1} (x)$ for the linear function $f (x) = 4 x - 5$ . Give your answers in the form $f^{- 1} (x) = m x + c$ .

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3H>Q 1

Find $f^{- 1} (x)$ for the linear function $f (x) = - \frac{1}{6} x + 3$ . Give your answers in the form $f^{- 1} (x) = m x + c$ .

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3H>Q 2

Find $f^{- 1} (x)$ for the linear function $f (x) = 0.25 x + 1.75$ . Give your answers in the form $f^{- 1} (x) = m x + c$ .

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3H>Q 3

The graph of a linear function $y = f (x)$ and the line $y = x$ is shown below. Copy the graphs and then add a sketch of the graph of $y = f^{- 1} (x)$ .

Question Image

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3H>Q 3

A t-shirt company imprints logos on t-shirts. The company charges a one-time set-up fee of $$ 65$ and $$ 10$ per shirt. The total cost of $x$ shirts, in $CAD$ , is given by $f (x) = 10 x + 65$ . Find the total cost for $55$ t-shirts.