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Math Help - Composite Function

  1. #1
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    Composite Function

    How to do these?
    The 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. g:x\rightarrow \ln x and gf:x\rightarrow 2 \ln (x+1)

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

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

    2. f:x\rightarrow x^2-1
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  2. #2
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    Quote Originally Posted by cloud5 View Post
    How to do these?
    The 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. g:x\rightarrow \ln x and gf:x\rightarrow 2 \ln (x+1)

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

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

    2. f:x\rightarrow x^2-1
    1.
     <br />
g(x)=ln (x)<br />
g(f(x))=2ln(x+1)=ln(x+1)^2 by the rules for logs

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

    2. g(x)=e^x
    g(f(x))=e^{x^2-1} so again g(?)= e^{x^2-1} and you should be able to look at that and see that it's x^2-1
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  3. #3
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    Quote Originally Posted by cloud5 View Post
    How to do these?
    The 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. g:x\rightarrow \ln x and gf:x\rightarrow 2 \ln (x+1)

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

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

    2. f:x\rightarrow x^2-1
    1. g(\textcolor{red}{x}) = \ln{\textcolor{red}{x}}

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

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

    f(x) = (x+1)^2


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

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

    f(x) = x^2-1
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