COMPOSITE FUNCTIONS Composite Functions When two functions are

COMPOSITE FUNCTIONS

Composite Functions When two functions are applied in succession, the resulting function is called the composite of the two given functions. Given f(x) = 8 x - 1 and g(x) = 3 x + 4, find the following: b)This (g otells f)(2)you to find the a) (f o g)(2) value g(x)= first, then use (g ooff)(x) g(f(x)) (f o g)(x) = f(g(x)) thisf(x) value = 8 xfor - 1 the function g(x) = 3 x + 4 f(x). f(2) Solve for-g(2). = 8(2) 1 g(2) = 3(2) + 4 = 15 = 10 With value of g(2) = 10, (g othe f)(2) = g(f(2)) you now solve for f(10). = g(15) (f o g)(2) = f(g(2)) g(2) = 10 g(x) = 3 x + 4 = f(10) g(15) = 3(15) + 4 f(x) = 8 x - 1 = 49 (f o g)(2) = 79 f(10) = 8(10) - 1 (g o f)(2) = 49 = 79

Composite Functions Example If you drop a pebble in a pond, a circular ripple extends out from the drop point. The radius of the circle is a function of time. The radius increases by eight inches per second. The area enclosed by the circular ripple is a function of the size of the radius. What’s the inside function? What’s the outside function? What’s composite function?

Composite Functions Domain and Range The domain of f of g of x is the set of all values of x in the domain of the inside function for which its results are in the domain of the outside function. The range is calculated by the limits of the domain placed on the outside function. WHAT!? !? !