Solve this C language question:

Consider the following $C$ function that computes the $n^{2h}$ Fibonacci number using recur$-$

sion:if $($n else $\{\}$

$\}($a$)(2$ points$)$ Write down a recurrence relation that describes the time complexity of

the above function in terms of $n.$

$($b$)(2$ points$)$ Use big$-O$ notation to express the asymptotic complexity of the function

based on your recurrence relation from part $($a$),$ and justify your answer.

$($c$)(1$ point$)$ The closed$-$form expression for the $n^{th}$ Fibonacei number is

$F(n)=\frac{{}^n-{}^n}{\sqrt[\phantom{2}]{5}}$

where $=\frac{1+\sqrt[\phantom{2}]{6}}{2}$ and $=\frac{1-\sqrt[\phantom{2}]{6}}{2}.$ What is the asymptotic time complexity of using

the closed$-$form expression, assuming multiplication is a constant$-$time operation?

Justify your answer.

$($d$)(5$ points$)$ Show that $({}^n)$ describes a tighter bound on the time complexity of

the recursive Fibonacci function above.