2b8ddf…: “Except a light calculation”

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1 : Consider the following functions: $f(x) = \sage {p1func1}$ and $g(x) = \sage {p1func2}$ . Compute:

$f(g(x)) = \answer {\sage {p1ans1}}$

$g(f(x)) = \answer {\sage {p1ans2}}$

$(f\circ g)(x) = \answer {\sage {p1ans1}}$

$((g\circ f)(x) = \answer {\sage {p1ans2}}$

You only need to compose the functions you do not need to simplify them. For example, if $f(x) = 13x^2 + x$ and $g(x) = \sqrt {x+1}$ then for $f(g(x))$ you would just copy in the “ $g(x)$ ” wherever there is an “ $x$ ” in $f(x)$ and leave it like that; i.e. you would input “ $13(\sqrt {x+1})^2 + \sqrt {x+1}$ . No need to simplify, reduce, or do anything else!

2 : Consider the following functions: $f(x) = \sage {p2func1}$ and $g(x) = \sage {p2func2}$ . Compute:

$f(g(x)) = \answer {\sage {p2ans1}}$

$g(f(x)) = \answer {\sage {p2ans2}}$

$(f\circ g)(x) = \answer {\sage {p2ans1}}$

$((g\circ f)(x) = \answer {\sage {p2ans2}}$

3 : Consider the following functions: $f(x) = \sage {p3func1}$ and $g(x) = \sage {p3func2}$ . Compute:

$f(g(x)) = \answer {\sage {p3ans1}}$

$g(f(x)) = \answer {\sage {p3ans2}}$

$(f\circ g)(x) = \answer {\sage {p3ans1}}$

$((g\circ f)(x) = \answer {\sage {p3ans2}}$

4 : Consider the following functions: $f(x) = \sage {p4func1}$ and $g(x) = \sage {p4func2}$ . Compute:

$f(g(x)) = \answer {\sage {p4ans1}}$

$g(f(x)) = \answer {\sage {p4ans2}}$

$(f\circ g)(x) = \answer {\sage {p4ans1}}$

$((g\circ f)(x) = \answer {\sage {p4ans2}}$

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norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
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Omega	$\Omega$

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