By the chain rule the temperature changes with time at a rate of & f(g(t)) = f'(g(t))g' (t) = degrees per hour. This exercise differs from the previous one in that I not only have to do the operations with the functions, but I also have to evaluate at a particular x -value. Fish enter a lake at a rate modeled by the function E given by E(1). Then calculate y (5x+7)8 Select the correct choice below and fill in the answer box to complete your choice. Hence f'(h) = Number The composite function f(g(t)) represents the temperature at time t. Given f (x) 2x, g(x) x + 4, and h(x) 5 x 3, find (f + g)(2), (h g)(2), (f × h)(2), and (h / g)(2). For the following composite function, find an inner function u g (x) and an outer function yf (u) such that yf (g (x)). The temperature drops at a constant rate of degrees for every kilometer above sea level. In mathematics, function composition is an operation that takes two functions f and g, and produces a function h g f such that h(x) g(f(x)).In this operation, the function g is applied to the result of applying the function f to x.That is, the functions f : X Y and g : Y Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. g'(t) 30° 13 Now let f(h) represent the temperature at h kilometers above sea level. The gradient of the mountain is 30 degrees (I told you it was steep!) If g(t) represents the altitude (in kilometers) of the car at time t (in hours) then, using the triangle below, we can calculate the rate of change in altitude as g' (t) = 5 kilometers per hour. f (x) x2 + 3x + 4 f ( x) x 2 + 3 x + 4, g (x) x 1 g ( x) x - 1, (g f) ( g f) Set up the composite result function.

A composite function is denoted by (g o f) (x) g (f (x)). For example, the function f: A B & g: B C can be composed to form a function which maps x in A to g (f (x)) in C. For example, suppose you drive a car up a steep mountain road at a constant speed of v = 10 kilometers per hour. In mathematics, the composition of a function is a step-wise application. It is not actually necessary to know an explicit formula for the functions f and g, only their derivatives are required. We have 2 functions that we will use for our composition: f(x) 2x g(x) x- 1 The flow chart below shows a step by step walk through of (f cdot g)(x). Transcribed image text: Remarkably, the chain rule allows you to calculate the derivative of the composite function f o g(x) = f(g(x)) as the product of the derivatives f'(g(x)) and g'(x).

Composite function calculator f g h