Review finding inverses and composite functions using square roots To find an inverse mathamaticaly there is one simple rule: Switch the x and y XY

Remember these f(x) = x/5 - 7 Find the domain and range of the function and its inverse. Domain of f(x) all real numbersDomain of f(x) x ≥ -4 Range of f(x) all real numbersRange of f(x) y ≥ 0 Domain f -1 all real numbers Domain f -1 x ≥ 0 Range f -1 all real numbersRange f -1 y ≥ -4 What do you notice?

Practice:

Composite functions review f(x) = 3x g(x) = 2x – 1 h(x) = 2x 2 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 – 2Ex. f(x) = 5x 2, x > 0 g(x) = √x/5 f o g = 2(3x – 2) – 3f o g = 5(√x/5) 2 f o g = 6x – 4 – 3f o g = 5(x/5) f o g = 6x – 7 not inverses.f o g = x g o f = √(5x 2 /5) g o f = √x 2 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) 4x 2 -1 x>0