# Composite Function

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• Jul 27th 2009, 04:38 AM
cloud5
Composite Function
How to do these?
The $\displaystyle e^x2-1$ is suppose to be e power of x then x power of 2-1, 2-1 is located above the x.

Find the function f
1. $\displaystyle g:x\rightarrow \ln x$ and $\displaystyle gf:x\rightarrow 2 \ln (x+1)$

2. $\displaystyle g:x\rightarrow e^x$ and $\displaystyle gf:x\rightarrow e^x2-1$

Answer:
1. $\displaystyle f:x\rightarrow(x+1)^2$

2. $\displaystyle f:x\rightarrow x^2-1$
• Jul 27th 2009, 05:55 AM
artvandalay11
Quote:

Originally Posted by cloud5
How to do these?
The $\displaystyle e^x2-1$ is suppose to be e power of x then x power of 2-1, 2-1 is located above the x.

Find the function f
1. $\displaystyle g:x\rightarrow \ln x$ and $\displaystyle gf:x\rightarrow 2 \ln (x+1)$

2. $\displaystyle g:x\rightarrow e^x$ and $\displaystyle gf:x\rightarrow e^x2-1$

Answer:
1. $\displaystyle f:x\rightarrow(x+1)^2$

2. $\displaystyle f:x\rightarrow x^2-1$

1.
$\displaystyle g(x)=ln (x) g(f(x))=2ln(x+1)=ln(x+1)^2$ by the rules for logs

So f(x) must be $\displaystyle (x+1)^2$ as g(?)= ln ? so the $\displaystyle ?=f(x)=(x+1)^2$

2. $\displaystyle g(x)=e^x$
$\displaystyle g(f(x))=e^{x^2-1}$ so again g(?)=$\displaystyle e^{x^2-1}$ and you should be able to look at that and see that it's $\displaystyle x^2-1$
• Jul 27th 2009, 05:58 AM
skeeter
Quote:

Originally Posted by cloud5
How to do these?
The $\displaystyle e^x2-1$ is suppose to be e power of x then x power of 2-1, 2-1 is located above the x.

Find the function f
1. $\displaystyle g:x\rightarrow \ln x$ and $\displaystyle gf:x\rightarrow 2 \ln (x+1)$

2. $\displaystyle g:x\rightarrow e^x$ and $\displaystyle gf:x\rightarrow e^x2-1$

Answer:
1. $\displaystyle f:x\rightarrow(x+1)^2$

2. $\displaystyle f:x\rightarrow x^2-1$

1. $\displaystyle g(\textcolor{red}{x}) = \ln{\textcolor{red}{x}}$

$\displaystyle g[f(x)] = 2\ln(x+1)$

$\displaystyle g[\textcolor{red}{f(x)}] = \ln{\textcolor{red}{(x+1)^2}}$

$\displaystyle f(x) = (x+1)^2$

2. $\displaystyle g(\textcolor{red}{x}) = e^{\textcolor{red}{x}}$

$\displaystyle g[\textcolor{red}{f(x)}] = e^{\textcolor{red}{x^2-1}}$

$\displaystyle f(x) = x^2-1$