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Combining Functions Section 1.7 Objectives • Determine the domain and range (where possible) of a function given as an equation. • Add, subtract, multiply, and/or divide function. • State the domain two function combined in an arithmetic method. • Put together two (or more) functions using composition. • Determine the value of the composition of two (or more) functions given the graphs of the functions. • Determine the value of the composition of two (or more) function given the equations of the functions. • State the domain two function combined through composition. Objectives • Decompose the composition of two functions into it constituent functions. • Solve a word problem involving the composition of functions. Vocabulary • domain • range • function composition Domain Questions 1. Does the function have a denominator? 2. Does the function have a square or even root? 3. Does the function have a log or ln in it? 4. Did the function arise from finding an inverse? 5. Is this a “real world” problem? Find the domain of the function: x 11 h (x ) 2 x 196 Find the domain of the function: f (x ) 67.5 5x Find the domain of the function: g (x ) 8x 2 4 Find the domain of the function: k (x ) 4 x 17 15 f (x ) x 5 Given the functions 8 and g (x ) x 9 find each of the following: (f g )(x ) (f g )(x ) (fg )(x ) f (x ) g 15 f (x ) x 5 Given the functions 8 and g (x ) x 9 find the domain of each of the following: (f g )(x ) (f g )(x ) (fg )(x ) f (x ) g For the functions f(x) and g(x) are given in the graph below. Find the indicated corresponding function values (f g )(1) (f g )(3) Given the functions f (x ) 6x 9 2 and g (x ) 3 x find each of each of the following: (f g )(2) ( g f )(2) 1 f (x ) x Given the functions and g (x ) 7x 6 find each of the following: (f g )(x ) ( g f )(x ) (f f )(x ) 1 f (x ) x Given the functions and g (x ) 7x 6 find the domain of each of the following: (f g )(x ) ( g f )(x ) (f f )(x ) For the functions f(x) and g(x) are given in the graph below. Find the indicated corresponding function values f ( g ( 3)) g (f (2)) Express the function h (x ) (x 5) 2 in the form f g . If f (x ) x , find g(x). 2 A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 9 cm per second. Express the surface area of the balloon as a function of time t (in seconds).