Composite and Inverse functions

Question # 1:

Is (f o g)(x) the same as (g o f)(x)?

Composite and Inverse functions

Question # 1 Answer:

No

Composite and Inverse functions

Question # 2:

What is the inverse of f(x) = 4x + 2

Composite and Inverse functions

Question # 2 Answer:

y = (x - 2)/4

Composite and Inverse functions

Question # 3:

If f(x) = sqrt (x), find in simplest form the composite function f(f(x)

Composite and Inverse functions

Question # 3 Answer:

sqrt 4 (x) 

Composite and Inverse functions

Question # 4:

If g(x) = 2 - x and f(x) = 4x, then find 'f o g' and 'g o f'

Composite and Inverse functions

Question # 4 Answer:

g o f = 2 - 4x

f o g = 8 - 4x

Composite and Inverse functions

Question # 5: 

What is the only time that f o g = g o f?

Composite and Inverse functions

Question # 5 Answer:

This case happens when 'g' is the inverse of 'f' or vice versa.

Composite and Inverse functions

Question # 6:

What is the domain and range of the function f(x) = sqrt (x)?

Composite and Inverse functions

Question # 6 Answer:

Domain: x > 0

Range: y > 0

Composite and Inverse functions

Question # 7:

f(x) = x^2, is the inverse a function?

Composite and Inverse functions

Question # 7 Answer:

No

Composite and Inverse functions

Question # 8:

What is a domain and a range of a function?

Composite and Inverse functions

Question # 8:

Domain are all input values whereas range are all output values.

Composite and Inverse functions

Question # 9:

How do you determine if a graphed line is a function or not?

Composite and Inverse functions

Question # 9 Answer:

The vertical line test.

Composite and Inverse functions

Information # 10:

A function has only one input value for every output value but it can have many output values for 1 input.

Composite and Inverse functions

Question # 11:

What is a composite function?

Composite and Inverse functions

Question # 11 Answer:

A composite function is a combination of two functions.