Saturday

August 23, 2014

August 23, 2014

Posted by **Jeff** on Sunday, December 8, 2013 at 3:12pm.

A.Solve each equation. Leave exact answers:

1.5^3x-2=14

2.log(x-1)-logx=log(x-3)

B.If f(x)=x+2/x and g(x)=7/x-5,

a. Find the composition (f o g)(x) and simplify completely.

b. Find the domain of (f o g)(x).Write answer in interval notation.

c. Find the composition of (g o f)(x) and simplify completely.

d. Find the domain (g o f)(x).Write your answer using interval notation.

- Math -
**Henry**, Monday, December 9, 2013 at 8:53pm1. 0.5^3x-2 = 14

0.5^3x = 14+2 = 16

Take Log of both sides:

3x*Log 0.5 = Log 16

Divide both sides by Log 0.5:

3x = Log 16/Log0.5 = -4

Divide both sides by 3:

X = -4/3

2. Log(x-1)-Log x = Log(x-3)

Log((x-1)/x) = Log(x-3)

B. f(x) = (x+2)/x; g(x) = 7/(x-5)

a. F(g(x)) = (7/(x-5)+2)/(7/(x-5)) =

(7+2(x-5)/(x-5))/(7/(x-5)) =

((2x-3)/(x-5))/(7/(x-5)) =

((2x-3)/(x-5))*(x-5)/7 = (2x-3)/7.

b. Domain: All real values of X.

-Infinity < X < +Infinity.

c. g(F(x)) = 7/((x+2)/x-5)=

7/(x+2-5x)/x = 7/(x+2-5x)/x =

7/(2-4x)/x = 7x/(-2(2x-1))

d. 2x-1 = 0

2x = 1

X = 1/2 Will result in a denominator of zero and the Eq becomes undefined.

DOMAIN: All real values of X except 1/2.

X <> 1/2.

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