2*=2^2+4=8
Option A (-2)*= (-2)^2+4=8
So option A is the answer.

Thank you.

Given that \(x* = x^2 + 4\) and we need to find the value of \(2*\)

To find \(2*\) we need to compare what is before * in \(2*\) and \(x*\)

=> We need to substitute x with 2 in \(x* = x^2 + 4\) to get the value of \(2*\)

=> \(2* = 2^2 + 4\) = 4 + 4 = 8

Now, the answer choices are also given in terms of * so we need to solve for each answer choice and check which one will be equal to 8.
Let's solve it using two methods

Method 1: Algebra

If we take a closer look at \(x* = x^2 + 4\) then we realize that x* is nothing but square of x + 4 = 8 (in case of 2*)
=> Square of x = 8 - 4 = 4
=> x = ± \(\sqrt{4}\) = ±2
=> x can be -2 also

So, Answer will be A

Method 2: Substitution

Lets take each option choice and check which one equates to 8

A) \((-2)* = (-2)^2 + 4\) = 4 + 4 = 8 => POSSIBLE
In exam we don't need to solve further but I am solving to complete the solution

B) \(0* = 0^2 + 4\) = 0 + 4 = 4 => NOT POSSIBLE

C) \(4* = 4^2 + 4\) = 16 + 4 = 20 => NOT POSSIBLE

D) \(6* = 6^2 + 4\) = 36 + 4 = 40 => NOT POSSIBLE

E) \(8* = 8^2 + 4\) = 64 + 4 = 68 => NOT POSSIBLE

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters