(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I keep getting what I think is the "right answer", but it's not one of my choices :^(

Here are the problems and answer choices.

1).

2).

2. Relevant equations

nothing really...or at least I don't think besides the fact that e^-x = 1/e^x

3. The attempt at a solution

1).

x + 14 = 2 g^( - 1) ( x )

(x + 14) / 2 = g^( - 1) ( x)

x - 3 = 4 f^( - 1) ( x)

( x - 3) / 4 = f^( - 1) ( x)

g^( - 1) o f^( - 1) ( x) = (x + 53) / 8

I get this for number 1, but it is not one of the answer choices!

2).

6 = 7e^x + e^(-x )

Let e^x = t, (t > 0), thus e^(-x) = 1/t

6 = 7t + 1/t

Multiplying each side by t

6t = 7t² + 1

7t² - 6t + 1 = 0

t = (3 ± √2)/7

e^x = t ==> x = ln (t)

x = ln [(3 + √2)/7] or x = ln [(3 − √2)/7]

I get this for number 2, but it is also not one of the answer choices!

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# Homework Help: Natural Logs and composition

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