Consider the following function.

f$($x$)=$

x $+7$x $1$

$,$x $>1$

What is the domain of f$?($Enter your answer using interval notation.$)$

Is f continuous on this domain?

YesNo$$

Find

f$\text{'}($x$).$

f$\text{'}($x$)=$

Does f have an inverse function?

YesNo$$

Consider the real number

a $=3.$

For what value of x does

f$($x$)=3?$

$($If an answer does not exist, enter DNE.$)$

x $=$

Determine the value of

f$1(3),$

if it exists. $($If an answer does not exist, enter DNE.$)$

f$1(3)=$

Use the function f and the real number

a $=3$

to find

$($f$1)\text{'}(3),$

if it exists. $($If an answer does not exist, enter DNE.$)$

$($f$1)\text{'}(3)=$