#### bumblebee123

##### Junior Member

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question: the function f is defined as f (x) = (x + 3) / (x - 1 )

find ff(x). give your answer in its simplest form.

any help would be really appreciated

- Thread starter bumblebee123
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question: the function f is defined as f (x) = (x + 3) / (x - 1 )

find ff(x). give your answer in its simplest form.

any help would be really appreciated

\(\displaystyle f(f(x)) = \frac{f(x)+3}{f(x)-1} = \text{???}\)

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I have a question. Was the question actually given as \(\displaystyle f\,f(x)~?\)can anyone help me to understand the answer to this question?

question: the function f is defined as f (x) = (x + 3) / (x - 1 ) find ff(x). give your answer in its simplest form.

OR was it written as either \(\displaystyle f\circ f(x)\) or \(\displaystyle f\cdot f(x)~?\)

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it was given as ff( x )I have a question. Was the question actually given as \(\displaystyle f\,f(x)~?\)

OR was it written as either \(\displaystyle f\circ f(x)\) or \(\displaystyle f\cdot f(x)~?\)

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so f ( f (x) ) = ( ( ( x+3) / ( x -1 )) + 3 ) / ( ((x +3 ) / ( x - 1 ) )) - 1)

\(\displaystyle f(f(x)) = \frac{f(x)+3}{f(x)-1} = \text{???}\)

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Yes, now do the algebra to simplify that.

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( 4x / (x-1) ) / ( 4 / (x-1) ) = ( 4x^2 - 4x) / ( 4x - 4) = ( 4 ( x^2 - x ) ) / ( 4 ( x-1) ) = (x^2 - x ) / ( x -1 ) = ( x ( x - 1) ) / ( x -1 ) = xYes, now do the algebra to simplify that.

so ff(x) = x which is correct

thanks

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