Math 36 Homework 1 Given that Soo 3x2 and ax1 gG 2 we S2216

Math 36 Homework 1. Given that Soo = 3x+2 and ax\"-1: gG)= 2. we S(-2,2),(-1,6),(48),0,-, (2,9)} set S= tepresents a (a) the domar C) S (S) What the relafionshi betwee, the lo one-to- one function. Fin (9) What relationrhip betee- he 3. Given that S and g are ln verse functions (a) 5-3)(x) b) g.sw.

Solution

1)
f = 3x + 2
g = 2x^2 - 1

fog :
f[g(x)]
f(2x^2 - 1)
which becomes

3(2x^2 - 1) + 2

6x^2 - 3 + 2

6x^2 - 1 ----> ANSWER

gof(-2) :

g(f(-2))

First f(-2) = 3(-2) +2 ---> -6 + 2 ---> -4

And now, g(-4) becomes :
2(-4)^2 - 1

2(16) - 1

32 - 1

31 ----> ANSWER

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2)
Domain : {-2 , -1 , 0 , 1 , 2}

Range : {-3 , 2 , 6 , 8 , 9}

S^-1 : {(2,-2) , (6,-1) , (8,0) , (-3,1) , (9,2)} --> just flip S

Domain of S^-1 = Range of S = {-3 , 2 , 6 , 8 , 9}

Range of S^-1 = Domain of S = {-2 , -1 , 0 , 1 , 2}

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3a)

If f and g are inverse...

Then fog(x) is

f[g(x)]

f[f^-1(x)]

which is x

gof(x) likewise is also x