1.1.205 AP calculus exam practice question

[karush]

given that
$\left[
f(x)=x-2,
\quad
g(x)=\dfrac{x}{x^2+1}\right]$
find $f(g(-2))$
(A) $\dfrac{-11}{5}$
(B) $\dfrac{-4}{17}$
(C) $-3$
(D) $\dfrac{14}{85}$
(E) $\dfrac{-12}{5}$
_____________________________________________________________________________

Solution
find $g(-2)$
$$\dfrac{-2}{(2)^2+1}
=\dfrac{-2}{5}$$
then solve $f(-2/5)$
$$\dfrac{-2}{5}-2
=\dfrac{-2}{5}-\dfrac{10}{5}
=\dfrac{-12}{5}\quad (E)$$

hopefully ok ... typos ... suggestions

is it possible to draw a horizonal line here \hline or \hrule not

also how do you use the hide/show option if you want to hide the solution

 

[Greg]

given that
$\left[
f(x)=x-2,
\quad
g(x)=\dfrac{x}{x^2+1}\right]$
find $f(g(-2))$
(A) $\dfrac{-11}{5}$
(B) $\dfrac{-4}{17}$
(C) $-3$
(D) $\dfrac{14}{85}$
(E) $\dfrac{-12}{5}$
_____________________________________________________________________________

Solution
find $g(-2)$
$$\dfrac{-2}{({\color{red}-2})^2+1}
=\dfrac{-2}{5}$$
then solve $f(-2/5)$
$$\dfrac{-2}{5}-2
=\dfrac{-2}{5}-\dfrac{10}{5}
=\dfrac{-12}{5}\quad (E)$$

hopefully ok ... typos ... suggestions

See stuff in red - otherwise looks good. :)

also how do you use the hide/show option if you want to hide the solution

Use [sp]...[/sp] tags.

 

[karush]

I don't see red stuff

 

[topsquark]

I don't see red stuff

Put your mouse in the quote box and scroll down.

-Dan