9) Suppose fíx) x and g(x) - 1-x. (objective 3 - algebraic operations on functio

Question

9) Suppose fíx) x and g(x) - 1-x. (objective 3 - algebraic operations on functions) a) What is (f-g)(x)? Answer: b) What is (fg)(x)? Answer: What is (f- g)(-1)? Answer: What is (fg)(6)? Answer: 10) If f(x) 2x +5 and g(x) 4x2+1, find the following compositions of these functions. (objective 3- algebraic operations on functions a) f g Answer: b) (f g)(3) Answer: c) g of Answer: 11)Find the inverse functions of the following functions. Then, verify that flf"(x) and f (fx)) x. (objective 3) b) f(x) = 4x + 9 Inverse function:-- Show that f(f(x)) x: Show that f(f(x))- x:

Explanation / Answer

f(x)=x2, g(x) =1-x

a. (f-g)(x) = x2-1 + x = x2+x -1

b.(f-g)(-1)=(-1)2-1-1=1-2=-1

c.(fg)(x) = x2(1-x) =x2-x3

d.(fg)(6)=62-63=36-216=-180

10. f(x)= 2x +5, g(x)=4x2+1

a. fog = f(g(x))= f(4x2+1) = 2(4x2+1)+5 = 8x2+7

b.(fog)(3)= 8(3)2+7= 79

c.gof= g(f(x))= g(2x+5)= 4(2x+5)2+1 = 16x2+80x+100 +1=16x2+80x+101

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