6 1 Operations on Functions EXAMPLE 1 Given

6. 1 Operations on Functions

EXAMPLE 1 Given f(x) = 3 x 2 + 7 x and g(x) = 2 x 2 – x – 1, find (f – g)(x).

EXAMPLE 2 Given f(x) = 2 x 2 + 5 x + 2 and g(x) = 3 x 2 + 3 x – 4, find (f + g)(x).

EXAMPLE 3 Given f(x) = 3 x 2 – 2 x + 1 and g(x) = x – 4, find (f ● g)(x).

EXAMPLE 4 Given f(x) = 2 x 2 + 3 x – 1 and g(x) = x + 2, find.

EXAMPLE 5 Given f(x) = x 2 and g(x) = Find the following. List any restrictions to domain or range. 1. (f + g)(x) 2. (f – g)(x) 3. (f ∙ g)(x) 4.

EXAMPLE 6 If f(x) = 2 x and g(x) = x 2 – 3 x + 2 and h(x) = -3 x – 4 then find each value. a. f[g(3)] b. g[h(-2)] c. h[f(-4)]

6. 1 Part 2 – Composite Functions

COMPOSITE FUNCTIONS Another way to combine functions is a composition of functions. In a composition of functions, the results of one function are used to evaluate a second function.

EXAMPLE 1 Find [f ○ g](x) for f(x) = 3 x 2 – x + 4 and g(x) = 2 x – 1. State the domain and range for each combined function.

EXAMPLE 2 Find [g ○ f](x) for f(x) = 3 x 2 – x + 4 and g(x) = 2 x – 1. State the domain and range for each combined function.

EXAMPLE 3 Find [f ○ g](x) and [g ○ f](x) for f(x) = x 2 + 2 x + 3 and g(x) = x + 5. State the domain and range for each combined function.

EXAMPLE 4 If f(x) = axm and g(x) = bxn, perform the operation stated. A) f(x) g(x) B) f(g(x)) C) g(f(x))

EXAMPLE 5 Hector has $100 deducted from every paycheck for retirement. He can have this deduction taken before state taxes are applied, which reduces his taxable income. His state income tax is 4%. If Hector earns $1500 every pay period, find the difference in his net income if he has the retirement deduction taken before or after state taxes.