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5.5: Perform Function Operations Algebra II 5.5: Perform Function Operations

Operations on Functions You have learned how to add, subtract, multiply, and divide polynomial expressions. These operations can also be defined for functions.

Operations on Functions Definition Addition (f+g)(x) = f(x)+g(x) Subtraction (f – g)(x) = f(x) – g(x) Multiplication (fg)(x) = Division

Example 1  

Example 2 Let f(x) = 3x3 – 2x2 + 5 and g(x) = x3 – 3x2 + 4x – 2 . Find (f – g)(x) and state the domain. Then evaluate the difference when x = -2.

Addition and Subtraction Let f(x) = x+5 and g(x) = x2 – 5x + 2 Find f(x) + g(x) Let f(x) = -3x1/3 + 4x1/2 and g(x) = 5x1/3 + 4x1/2 Find f(x) – g(x)

Example 3  

Example 4  

Multiplication and Division Let f(x) = 4x2/3 and g(x) = 5x1/2 Find g(x) . f(x) Find g(x)/f(x)

Do Now: f(x)=4x1/2, g(x)=-9x1/2, h(x)=6x, m(x)=x3/4 f(x) + g(x) h(x)m(x) h(x)/m(x)

Composition of Functions Find the following: f(0) = g(0) = f(1) = g(1) = f(20) = g(20) = Think: f(g(x)) g(f(x))

Composition of Functions The composition of a function g with a function f is: h(x) = g(f(x))

Perform the indicated operation. Let f(x) = 2x2 and g(x) = 3x – 5 Find g(f(x)) Find f(g(x))

Find the indicated value. Let f(x) = 4x + 7 and g(x) = 12x – 1 Find g(f(3)) Find f(g(3))

Find the indicated value. Let g(x) = -x2 and h(x) = Find h(h(-4)) Find g(h(8))

Perform the indicated operation. Let f(x) = 2x2 – x , g(x) = , and h(x) = Find f(g(x))

Perform the indicated operation. Let f(x) = 2x2 – x , g(x) = , and h(x) = Find g(h(x))

Perform the indicated operation. Let f(x) = 2x2 – x , g(x) = , and h(x) = Find f(h(x))