# Function Operations

Given the following functions, evaluate each of the following: f(x) = x2 – 2x – 8 g(2) = x – 4 (f +9)(-3) = (f-9)( – 4) = (fºg)(4) = = (9) ( – 5) = = Function Operations Given the functions: f(x) = 5x g(x) = 2x + 9 h(x) = 12×2 + 46% 36 Determine each of the following. Give your answers as simplified expressions written in descending order. g(x) + h(x) = Find and simplify g(x) + h(2) h(x) – g(x) = Find and simplify h(c) – 9(2) f(x) h(x) = Find and simplify f(x).h(2) h(2) g(x) = 1 h(2) Find and simplify hint: you will need to g(2) factor h(x) g(x) The domain restriction for is f(a) x + Given that f(x) = 8x + 7 and g(2) = 7 – x2, calculate (a) f(g(0)) = (b) g(f(0)) = Use the graphs to evaluate the expressions below. 6+ f(x) 5 8(x) 5 4 4 3 3 2 N 1 1 х х -1 1 2 3 4 5 6-1 1 2 3 4 5 & F-1 f(g(2)) g(f(4) = = f(f(0) = g(g(3)) = Let f() = 5x + 5 and g(x) = 2×2 + 3x. After simplifying, (fog)(x) = Question oln. Video Let f(x) = 1 X – 2 – 4 + 2. and g(2) = Find the following functions. Simplify your answers. f(g(x)) = g(f(x)) = Move the slider k so that the graph of y = x2 gets shifted up 3 units. Then type the new function, f(x) in the answer box 6 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 f(x) = x2 k= 0.00 -2 o + Don’t forget to shift the graph up. Using function notation, i.e. f(x) = , enter the function that results from the transformation. Move the slider h so that the graph of y = x2 gets shifted to the right 3 units. Then type the new function, f(a) in the answer box 4 3 2 1 -4 -3 -2 – 1 0 1 2 3 4 f(x) = x2 -1 O h = 0.00 -2 – O ++ 1个 1 1 → Don’t forget to shift the graph to the right. Using function notation, i.e. f(x)=, enter the function that results from the transformation. Move the sliders h and k so that the graph of y x2 gets shifted up 2 units and to the right 1 units. Then type the new function, f(x) in the answer box 4 3 2 1 -4 -3 -2 -1 0 1 2 3 4 f(x) = 2 = 2 x2 -1 h = 0.00 -2 k= 0.00 – 0 ++ → Don’t forget to shift the graph. Using function notation, i.e. f(x) = , enter the function that results from the transformation. 5 3 2 1 -5 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 -5+ Write an expression for the function graphed above: Enter abs(x) for (x). 6 5 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 -2 -5 -6 The graph above is a transformation of the function x2. Give the function in the graph above. g(x) = Assume that the function f is a one-to-one function. (a) If f(2) = 9, find f-1(9). Your answer is (b) If f-‘(- 6) = -5, find f(-5). Your answer is Let f(x) = (x – 2)2 Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f restricted to this domain. f-1(x) = Let f(x) = x + 2 and g(x) = x – 2. With the following stephs, determine whether f(x) and g(x) are inverses of each other: (a) f(g(x)) = (b) g(f(x)) = (c) Are f(x) and g(2) inverses of each other?

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