Assignment 9

Assignment 9 - Assignment #9 Section 4.2 1b) f o g =...

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Assignment #9 Section 4.2 1b) f o g = 4x^2+8x+3 g o f = 2x^2+4x+1 2b) Dom f o g = R Rng f o g = [-1,infinity) Dom g o f = R Rng g o f = [-1, infinity) 3b) Inv(f) = ((x-1)/2)^(0.5) Not a function. 4) Suppose f:A->B a) Dom(Ib o f) = Dom(f) = A b) If x is an element of A, (Ib o f)(x) = Ib(f(x)) = f(x). By a) and b) Ib o f = f. 7c) {(x,y) is an element of RxR : y = -x} {(x,y) is an element of RxR : y = |x-1| - 1} 12b) Function. 12e) Not a function. 14c) h is increasing on [0, inf) where h(x)=x^2 Suppose x and y are in [0,inf) s.t. x < y. It follows that x^2 < y^2, so h(x)<h(y) 14g) f is increasing on I where f=g o h, h is increasing on I, and g is increasing on h(I). Suppose x, y are in I s.t. x<y Since h is increasing h(x)<h(y) It follows that g(h(x))<g(h(y)) as g is increasing on h(I). This is equivalent to g o h(x)<g o h(y) so f(x)<f(y), so f is increasing. 15b) False: Let f(x)=g(x)=-x on the interval [-1,1]. Then f and g are decreasing but (f o g)(x)=x so f o g is not decreasing. 19b) A.
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Assignment 9 - Assignment #9 Section 4.2 1b) f o g =...

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