Simplified ans--- (Infinity,-4] union [4, infinity)
Fun fact: f(x) represents the upper half of a hyperbola. To see this, note that the equation for a hyperbola has the standard form (x/a)^2 - (y/b)^2 = 1. In this case, a=b=4. Substituting this in and solving for y gives that y = +/- sqrt(x^2 - 16). To obtain a function of x (as this result is a relation but not a function), you simply choose either the positive or negative square root.
ok but why did we flipped sign for negative value ?
Domain is [-infinity,-4], [4,+infinity]
domain expansion
(-4,-infinity)u(+4,,+infinity)
but 4 is a working number , b/c when you square 4 and decrease 16 it gives you 0, and zero of square root is zero so it should be D=R / (-4,4)
You are not finding the domain but rather the domain when the range is the real numbers
There’s no problem mathematically to have a function over the imaginary numbers. In fact it is required in many engineering disciplines
So (-inf,-4]U[4,inf)
A better solution would be taking whole x²-16 greater than or equal to zero then use wavy curve method to find the solution
Plz also solve for range ... Plz
How to you determine the inequalities signs? Like why x>4 not 4>x ?
Wouldn't it be better to say x²>16 |x|>4 x>4 or x<-4 I know there should be a "greater than or equal to" instead of "greater than" symbol but I don know how to write that.
Of course I had to get it now after the test
R - (-4,4)
So is f of x 4 or -4
what if you have this: x times square root of: x^2 - 16
Can you say |x|>=(greater than or equal to)4?
@4thsanninn