$7.($a$)($a$)$ Write a MATLAB script that evaluates the function:

$f(x)=\sqrt[\phantom{2}]{x^2+1}-x$

for $x$ values between ${10}^7$ and ${10}^8,$ using $1000$ equally spaced points, use the linspace function to

generate your grid. Plot the $f(x)$ and observe its behavior for those values of $x.$

$($b$)$ Does the function behave as expected? Why or why not?

$($c$)$ Rewrite the function to correct the issue.

$($d$)$ Modify your MATLAB script to plot both the original function and the rewritten function on the

same graph for comparison.

Write a MATLAB script that evaluates the function: f$($x$)=$px$2+1$x

for x values between $107$ and $108,$ using $1000$ equally spaced points, use the linspace function to generate your grid. Plot the f$($x$)$ and observe its behavior for those values of x$.$

$($b$)$ Does the function behave as expected? Why or why not?

$($c$)$ Rewrite the function to correct the issue.

$($d$)$ Modify your MATLAB script to plot both the original function and the rewritten function on the same graph for comparison.