what's the domain and the range of f(x)= square root of 4-x^2

Question

anonymous · Answer

under radical must be non negative

anonymous · Answer

$$f(x)=\sqrt{4-x^2}$$

anonymous · Answer

4 - x^2 > = 0

anonymous · Answer

Solve for x

anonymous · Answer

so the answer would be x=2 or -2 ??????

anonymous · Answer

So.... Domain = [ -2 ,2]

anonymous · Answer

@mukushla  am i correct..))

anonymous · Answer

yes u are...
fatemah do u know why? D=[-2,2]

anonymous · Answer

yes because less or more than these values will give us negative values which cant be put under an even root :) so whats the value of the range??

anonymous · Answer

ok :) make 'x' ur subject..and of course we know domain of inverse function is range of function itself

anonymous · Answer

$$y=\sqrt{4-x^2}$$there is a restriction here y>=0

solve for x$$y^2=4-x^2$$$$x^2=4-y^2$$$$x=\sqrt{4-y^2}$$

anonymous · Answer

so the range is also = [-2,2] ???

anonymous · Answer

we had a restriction before doing inverse stuff$$y=\sqrt{4-x^2}$$this implies that $$y \ge0$$

anonymous · Answer

so whats the value of the range??

anonymous · Answer

[0,2]  why?

anonymous · Answer

so the values of the domain will give us 0 , 1 or 2 ????

anonymous · Answer

every number between 0 and 2  :)