Review finding inverses and composite functions using square

rootsTo find an inverse mathamaticaly there is one simple rule: Switch the x and y

X Y

Remember thesef(x) = x/5 - 7

Find the domain and range of the function and its inverse.

Domain of f(x) all real numbers Domain of f(x) x ≥ -4Range of f(x) all real numbers Range of f(x) y ≥ 0

Domain f-1 all real numbers Domain f-1 x ≥ 0Range f-1 all real numbers Range f-1 y ≥ -4

What do you notice?

Practice:

Composite functions reviewf(x) = 3x

g(x) = 2x – 1 h(x) = 2x2

f ○ g (2) or f(g(x))

This is 2 problems in one first find g(2) then take that answer and find f(answer).

g(2) = 2(2) – 1 = 3

f(3) = 3(3) = 9

h ○ g (-1)=g(-1) = 2(-1) – 1 = -3 h(-3) = 2(-3)2 = 18

F(h (5))=h(5) = 2(5)2 = 50 f(50) = 3(50) = 150

We can use composite functions to determine if two functions are

inverses.If f o g = x and g o f = x then f and g are inverses.

Ex. f(x) = 2x – 3 g(x) = 3x – 2 Ex. f(x) = 5x2, x > 0 g(x) = √x/5

f o g = 2(3x – 2) – 3 f o g = 5(√x/5)2

f o g = 6x – 4 – 3 f o g = 5(x/5)f o g = 6x – 7 not inverses. f o g = x

g o f = √(5x2/5)g o f = √x2

g o f = x inverses

We can use composite functions to determine if two functions are

inverses.If f o g = x and g o f = x then f and g are inverses.

practice. f(x) = √(x + 1)/4 g(x) 4x2 -1 x>0