According to this rational function
$$ f(x) = \frac{x + \frac{3}{8}}{x+ \frac{2}{5}} $$
what is $f(1/4)$?
My choices: $\frac{35}{52}$, $1$, $\frac{52}{30}$, $\frac{20}{9}$, $\frac{9}{2}$
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On such a basic problem, you need to show an attempt. Evaluating $f1/4)$ means to replace all occurrences of $x$ by $1/4$. Let's see you try it. – quasi May 31 '19 at 05:36
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3All the choices given are wrong. Let us know what your answer is and we can then confirm it. – Kavi Rama Murthy May 31 '19 at 05:37
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1Books (or handouts) can have errors -- still, you need to show what you tried -- that's expected on this site. – quasi May 31 '19 at 05:44
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Hint: you need to evaluate the function at $x=1/4$. This means putting the value $1/4$ in the place of $x$, resulting in $$ f \left( \frac{1}{4} \right) = \frac{ \frac{1}{4} + \frac{3}{8} }{ \frac{1}{4} + \frac{2}{5}} $$ Now you only need to simplify this. – Matti P. May 31 '19 at 05:58
3 Answers
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top: $$\frac{2}{8}+\frac{3}{8}\ = \frac{5}{8}$$
bottom: $$\frac{5}{20}+\frac{8}{20}\ = \frac{13}{20}$$
answer: $$\frac{100}{104}$$
not sure where you're getting your options from but this is the correct answer without reducing
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2Thanks for proving the answers given to me by this ACT precalc practice test wrong. – Lucius Irving May 31 '19 at 06:43
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Welcome to MSE! $$f(x) = \frac{x + \frac{3}{8}}{x+ \frac{2}{5}}$$ Just put the value $x=1/4$ $$f(1/4)= \frac{\frac{1}{4}+\frac{3}{8}}{\frac{1}{4}+\frac{2}{5}}$$.
Simplify it and you will have your answer.
Vineet
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Simply multiply numerator and denominator by $40$ to get $$\frac{\frac14 + \frac{3}{8}}{\frac14+ \frac{2}{5}}=\frac{40\cdot\left(\frac14 + \frac{3}{8}\right)}{40\cdot\left(\frac14+ \frac{2}{5}\right)} =\frac{10+15}{10+16}.$$
Michael Hoppe
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