Understanding Functions and Inverses

The video tutorial explains the concept of functions, focusing on linear equations and their gradients. It demonstrates how to find the inverse of a function by swapping inputs and outputs, and how to rewrite equations to make y the subject. The tutorial introduces function notation for clarity and demonstrates the inverse function with examples, showing how it reverses the input-output process.

What is the gradient of the function 3x + 1?

• 2

• 1

• 3

• 4

Where does the function 3x + 1 intersect the y-axis?

• At 3

• At 2

• At 1

• At 0

How do you find the inverse of a function?

• By swapping inputs and outputs

• By subtracting 1 from the function

• By multiplying the function by 2

• By adding 1 to the function

What is the first step in making y the subject in the equation x = 3y + 1?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 1 from both sides

• Add 1 to both sides

What is the final form of the inverse function after rewriting it?

• y = x - 1

• y = 3x + 1

• y = 3(x - 1)

• y = (x - 1) / 3

What does the notation f^(-1)(x) represent?

• The derivative of f(x)

• The reciprocal of f(x)

• The inverse of f(x)

• The integral of f(x)

Why is function notation useful?

• It makes equations longer

• It makes calculations more complex

• It is only used in advanced mathematics

• It helps distinguish between a function and its inverse

What is the output of f(5) if f(x) = 3x + 1?

• 17

• 15

• 16

• 14

If f(x) = 3x + 1, what should f^(-1)(16) return?

• 5

• 4

• 6

• 7

What is the purpose of an inverse function?

• To halve the input

• To reverse the input-output process

• To double the output

• To square the output