Composite and inverse functions

Question 1

Composite functions

Answer 1

Write out equations in form f(g(x)) for example
Then sub g(x) in.
Then in the the f(x) function, find every x and substitute g(x) in.

Question 2

Inverse functions

Finding formula of inverse function

Answer 2

Change h(x) (example) to y.
Then change subject of formula from y to x.
Then rewrite again keeping formula the same but swapping x for y and vice versa.
Finally swap the y = back to h^-1(x) =

Question 3

Showing functions are inverse of one another

Answer 3

Do composite functions with the two and if it simplifies to x on its own then they are inverse

Question 4

Drawing inverse functions

Answer 4

Swap y and x coordinates - (4,6) —> (6,4)

Graph shape will also be similar