In a problem like this, simply do a find and replace with the x into whatever the function is. In this case, every time you see an *, replace whatever is under it with the x in the given function. Since this one is nested in two sets of parenthesis, let's do the inside set first.

The inside-most function is -π*, so we should replace the x in the given function with -π. Thus, we get:

π/-π = -1

Now, the outer-most function is whatever result we got from the last function. So we have -1*. Repeat:

π/-1 = -π

So the answer is C.
_________________

still can,t understand, someone help me please in an another way.
_________________

\(x^*=\frac{\pi}{x}\)


Now the x^* on the left-hand side basically is the \(- \pi\) inside the parenthesis because notice the similarity \(x^*=- \pi^*\)

so \(\frac{\pi}{-\pi} =-1\)

and repeat the process once again.

Hope this helps
_________________

still confuse
_________________

_________________

GIVEN: \(x* = \frac{\pi}{x}\)

for example, \(10* = \frac{\pi}{10}\)

\(7* = \frac{\pi}{7}\)

\(4.6* = \frac{\pi}{4.6}\)

To calculate \((- \pi^*)^*\), we must first deal with the part in the brackets, \((-\pi^*)\)


\(-\pi^* = \frac{\pi}{-\pi} = -1\) just like \(\frac{3}{(-3)} = -1\), and \(\frac{22}{(-22)} = -1\)

Now that we know \(-\pi* = -1\), we can write: \((-\pi^*)^* = (-1)^*\)


Now, we'll calculate \((-1)^*\)

\(-1^* = \frac{\pi}{-1}= -\pi\) just like \(\frac{8}{(-1)} = -8\), and \(\frac{5.5}{(-1)} = -5.5\)

Answer: C

Cheers,
Brent
_________________

Many Many thanks
_________________

Stunning explanation
_________________