Question

Find the domain and range of the function f(x) = √(16-x2).

Answer 1

F(x)=√(16-xsq)

For Domain
√(16-xsq)=0

16-xsq=0

xsq= 16

x= +-4
So Domain= R-{+4,-4} Ans

For Range
y= √16-xsq

ysq= 16-xsq

xsq = 16-ysq

x= √16-ysq

For Range

√16-ysq=0

16-ysq=0

y= +-4

So Range = R-{+4,-4} Ans

Answer 2

Answer:

$D=(-4,4) , x|-4\leq x\leq 4$

$R=(0,4) , y|0\leq y\leq 4$

Step-by-step explanation:

Given : The function $f(x)=\sqrt{16-x^2}$

To find : The domain and range of the function?

Solution :

Domain of the function is where the function is defined  

The given function $f(x)=\sqrt{16-x^2}$

To find domain,

$\sqrt{16-x^2}=0$

$16-x^2=0$

$x^2=16$

$x=\pm4$

So, Domain of the function is $D=(-4,4) , x|-4\leq x\leq 4$

Range is the set of value that corresponds to the domain.

f(x) is maximum at x=0 , f(x)=4

f(x) is minimum at x=4 , f(x)=0

So, Range of the function is $R=(0,4) , y|0\leq y\leq 4$