Question $1$ Let $f(x)=\sqrt[\phantom{2}]{x^2+9}-3$ and $g(x)=\frac{x^2}{\sqrt[\phantom{2}]{x^2+9}+3}.$

$($a$)$ Use either Matlab or Python $($your choice$)$ to write a separate function

for each. Use the functions to calculate $f(x)$ and $g(x)$ for the input values

$x=\frac{1}{4},\frac{1}{4^2},\frac{1}{4^3},$cdots,$\frac{1}{4^{20}}.$ You should display your results clearly as three

columns $-x,f(x),g(x).$ Your code must be well$-$commented. Submit your

code and output as a pdf$.$

$($b$)$ Show $($by hand$)$ that $f(x)=g(x).$

$($c$)$ Although $f(x)=g(x),$ your computer should give different results. Ex$-$

plain why this happens, and which calculation is more reliable and why.