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Algebra of Functions. Review. Function notation: f(x) This DOES NOT MEAN MULITPLICATION. Given f(x) = 3x - 1, find f(2). Substitute 2 for x f(2) = 3(2) - 1 = 6 - 1 = 5. Review. Given f(x) = x - 5, find f(a+1) f(a + 1) = (a + 1) - 5 = a+1 - 5 f(a + 1) = a - 4. Objectives.
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Review • Function notation: f(x) • This DOES NOT MEAN MULITPLICATION. • Given f(x) = 3x - 1, find f(2). • Substitute 2 for x • f(2) = 3(2) - 1 = 6 - 1 = 5
Review • Given f(x) = x - 5, find f(a+1) • f(a + 1) = (a + 1) - 5 = a+1 - 5 • f(a + 1) = a - 4
Objectives • To define the sum, difference, product, and quotient of functions. • To form and evaluate composite functions.
Basic function operations • Sum • Difference • Product • Quotient
Function operations • If and find:
Function operations • If and find:
Function operations • If and find:
Function operations • If and find:
Function Composition • Function Composition is just fancy substitution, very similar to what we have been doing with finding the value of a function. • The difference is we will be plugging in another function
Function Composition • Just the same we will still be replacing x with whatever we have in the parentheses. • The notation looks like • We read it ‘f of g of x’
Composition of functions • Composition of functions is the successive application of the functions in a specific order. • Given two functions f and g, the composite functionis defined by and is read “f of g of x.”
x f Function Machine Function Machine g A different way to look at it…
