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There are **16** NRICH Mathematical resources connected to **Functions and their inverses**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### Real-life Equations

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Spaces for Exploration

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

Age 11 to 14

Problem
Primary curriculum
Secondary curriculum
### Area L

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Function Pyramids

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rational Request

Can you make a curve to match my friend's requirements?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Inverting Rational Functions

Consider these questions concerning inverting rational functions

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maths Shop Window

Make a functional window display which will both satisfy the manager and make sense to the shoppers

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curve Match

Which curve is which, and how would you plan a route to pass between them?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pitchfork

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Double Time

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Readme

Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrange the formula and use the inverse to decipher automatically.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Number Crunching Machine

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Age 7 to 11

Challenge Level