## Simple explanation of Functions

A function is really just another way of writing an equation. A function is a way to analyse two unrelated set of numbers.

## Functions Basics

Functions are a way of writing a process that happens to a number. For example, if I wanted to multiply my original number by 3, then subtract 6, I could write it as this function:

**f(x) = 3x-6.**
So if my original number was 10:
f(10) = 3(10)-6 f(10) = 30-6 f(10) = 24 |
Or if the original number was -12
f(-12) = 3(-12)-6 f(-12) = -36-6 f(-12) = -42 |

In the exam, they may phrase this type of question as "Evaluate f(10)" or "Evaluate f(-12)". This is the same type of question as shown above.

Trickier Questions

For the questions below, lets use these two functions:

**f(x) = 2x+3****g(x) = 7-4x**
1) What is gf(4)?This is the same as g(f(4)). So first, lets find f(4): f(4) = 2(4)+3 f(4) = 8+3 f(4) = 11 Now we need to find g(11) g(11) = 7-4(11) g(11) = 7-44 g(11) = -37 Answer = -37 |
2) Evaluate f²(2)This is the same as f(f(2)) So first, lets find f(2) f(2) = 2(2)+3 f(2) = 4+3 f(2) = 7 Now we need to find f(7) f(7) = 2(7)+3 f(7) = 14+3 f(7) = 17 Answer = 17 |
3) Solve f(x)=2g(x)We need to substitute in f(x) and g(x), then simplify: 2x+3 = 2(7-4x) 2x+3 = 14-8x To find x, we need to make it the subject: 10x+3=14 [added 8x] 10x=11 [subtracted 3] x=1.1 [divided by 10] Answer = 1.1 |

Inverse Functions

Inverse Functions are the reverse of normal functions. For example, I have the function 2x+3. This function gives me the answer when I input a number. But what if I wanted to find the original number from the answer? Say I have the answer of 49. I now want to know the function that would lead me to the original number - in other words, the inverse function of 2x+3:

First, let y=2x+3. Then make x the subject of this equation:

y=2x+3

2x=y-3

x=(y-3)÷2

Then, substitute the 'x' for a 'f^-1(x)' and the 'y' for an 'x' to get the inverse function:

f^-1(x) = (x-3)÷2

Since we already had the answer of 49, we place it in our inverse function to calculate the original number:

(49-3)÷2

46÷2 = 23

Use this method to get the inverse function or the original number

First, let y=2x+3. Then make x the subject of this equation:

y=2x+3

2x=y-3

x=(y-3)÷2

Then, substitute the 'x' for a 'f^-1(x)' and the 'y' for an 'x' to get the inverse function:

f^-1(x) = (x-3)÷2

Since we already had the answer of 49, we place it in our inverse function to calculate the original number:

(49-3)÷2

46÷2 = 23

**Answer = 23**Use this method to get the inverse function or the original number

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## Functions questions for Teachers

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