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Please help. I am not sure how to go about this.

Please help. I am not sure how to go about this.-example-1

1 Answer

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Solution:

(a) Given the functions:


\begin{gathered} f(x)=x-4 \\ \\ g(x)=x+4 \end{gathered}

Then:


\begin{gathered} f(g(x))=f(x+4) \\ \\ f(x+4)=x+4-4 \\ \\ f(g(x))=x \end{gathered}

Similarly,


\begin{gathered} g(f(x))=g(x-4) \\ \\ g(x-4)=x-4+4 \\ \\ g(f(x))=x \end{gathered}

Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.

ANSWER: f and g are inverse of each other.

(b) Given:


\begin{gathered} f(x)=-(1)/(3x),x0 \\ \\ g(x)=(1)/(3x),x0 \end{gathered}

Then:


\begin{gathered} f(g(x))=f((1)/(3x)) \\ \\ f((1)/(3x))=-(1)/(3((1)/(3x))) \\ \\ f(g(x))=-x \end{gathered}

Also,


\begin{gathered} g(f(x))=g(-(1)/(3x)) \\ \\ g(-(1)/(3x))=(1)/(3(-(1)/(3x))) \\ \\ g(f(x))=-x \end{gathered}

ANSWER: f and g are not inverses of each other.

User Prashant Gami
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