Snhu
MODULE FIVE PROBLEM SET
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Noyal Reji Jacob
snhu
Directions: Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit.
PROBLEM 1
Indicate whether the two functions are equal. If the two functions are not equal then give an element of the domain on which the two functions have different values.
(a)
f :Z Z, where f(x) =x2 g :Z Z, where g(x)=|x|2
f(x) = x2 g(x)=|x|2 bothfunctionsaresameas|x|2andx2givesapositivevalue.f : ZZ Z, where f(x,y) = Ix+ yl. |f|+|x|=(fx)6aI0qMZZXZ:6
f(x,y)= - x + y g(x,y)= Both functions aren't equal if either of x or y are of opposite sign Let x = -1 y=1 f(x,y) = 1-1= 0 g(x,y) = 1 + -1 = 2
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PROBLEM 2
The domain and target set of functions f and g is R. The functions are defined as:
(b) f(x)=2x+3
g(x)=5x+7
(a) fog?
f og(x)=f(g(x)) =f(5x+7)+3 =2(5x+7)+3 = 10x + 14 + 3 = 10x + 17 f og(x)=10x+17 (b) gof?
gof(x)=g(f(x)) = g(2x + 3) =5(2x +3)+7 =10x +15+7 = 10x + 22 g o f(x) = 10x +22(fog)-1?
Let f og(x)=y soy = 10x + 17 Tofindtheinverse,swapxandyandsolvefory sox =10y+17 y = x - 17/10 f o g(x)= x - 17/10
(c) f-1o g-1?
f(x) = 2x + 3 = y swap x and y and solve for y x = 2y+ 3 y = x - 3/2 f-1x)=x-3/2 9(x)=5