MathRevolution wrote:
[GMAT math practice question]
\(f(2x-1) = \frac{( x + 2 )}{( x – 2 )}\). What is \(f(x)\)?
\(A. f(x) = \frac{( x + 5 )}{( x – 3 )}\)
\(B. f(x) = \frac{( x - 5 )}{( x + 3 )}\)
\(C. f(x) = \frac{( x + 5 )}{( x + 3 )}\)
\(D. f(x) = \frac{( x – 5 )}{( x – 3 )}\)
\(E. f(x) = \frac{( x + 3 )}{( x – 3 )}\)
\(? = f\left( x \right)\)
\(f\left( {2x - 1} \right) = {{x + 2} \over {x - 2}}\,\,\,\,\,\left( * \right)\)
\(2x - 1 = y\,\,\,\,\, \Rightarrow \,\,\,\,x = {{y + 1} \over 2}\)
\(\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,f\left( y \right)\,\, = \,\,{{{{y + 1} \over 2} + 2} \over {{{y + 1} \over 2} - 2}}\,\, = \,\,{{y + 1 + 4} \over {y + 1 - 4}} = {{y + 5} \over {y - 3}}\)
\(?\,\,\,:\,\,\,f\left( y \right) = {{y + 5} \over {y - 3}}\,\,\,\,\,\,\,\left[ {\,f\left( x \right) = {{x + 5} \over {x - 3}}\,\,\,{\rm{if}}\,\,{\rm{you}}\,\,{\rm{prefer}}!\,} \right]\)
The correct answer is therefore (A).
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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