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# 2.1. Univariate Calculus: Functions and inverses

### Learning Objectives

You should be able to

• recognise and use function notation and terminology
• find the inverse to a function

### Get Started: What to do next

If you can pass the diagnostic test, then we believe you are ready to move on from this topic.
Our recommendation is to:
1. Test your ability by trying the diagnostic quiz. You can reattempt it as many times as you want and can leave it part-way through.
2. Identify which topics need more work. Make a note of any areas that you are unable to complete in the diagnostic quiz, or areas that you don't feel comfortable with.
3. Watch the tutorials for these topics, you can find these below. Then try some practice questions from the mini quiz for that specific topic. If you have questions, please ask on the forum.
4. Re-try the diagnostic quiz. And repeat the above steps as necessary until you can pass the diagnostic test. A pass grade is 80%.

Optionally, also see if you can apply these skills to an economic application or look at the additional resources and advanced quizzes at the bottom of the page,

### Tutorials: How to guides

#### 2.1.1. Introduction to functions

Terminology and notation relating to functions.

#### 2.1.2. Inverses of functions

How to compute an inverse $$f^{-1}$$ to a function.

### Economic Application: Demand and inverse demand

How much of a good is demanded in a market will depend on its price. The relationship between quantity demanded and the price of the good is described by a demand function. It is usually reasonable to think that higher prices lead to reduced demand. On the other hand the same relationship can be specified by means of an inverse demand function, the inverse of the demand function. The inverse demand function takes a quantity of the good as argument and returns the price that a seller should set in order to be able to sell this quantity (i.e. in order for consumers to demand as much of the good). The following application considers how inverse demand functions can be obtained from the corresponding demand functions and their economic interpretation.

#### 2.1.3. Economic Application Example

CORRECTION: At around 9:38

$$p_b^{0.36} = \frac{92}{q_b}$$ (note the sign of the exponent of $$p_b$$ is corrected here) so the inverse demand function should be $$p_b(q_b) = \left(\frac{92}{q_b}\right)^{\frac{1}{0.36}}$$

#### Economic Application Exercise

The following quiz allows you to test your understanding of interpreting demand and inverse demand functions and obtaining the inverse demand function from a given demand function.

### Further practice & resources

You can find practice quizzes on each topic in the links above the tutorial videos, or you can take the diagnostic quiz as many times as you like to If you want to test yourself further, then try the advanced quiz linked below.

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