What is the domain and range of $y = 5 - (\sqrt{9 - x^{2}})$ $y = 5 - (sqrt(9-x^2))$ ?

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Answer 1 · 2018-02-26T04:34:01

Donain: $[- 3, + 3]$ $[-3,+3]$ Range: $[2, 5]$ $[2, 5]$

$f (x) = 5 - (\sqrt{9 - x^{2}})$ $f(x) =5-(sqrt(9-x^2))$

$f (x)$ $f(x)$ is defined for $9 - x^{2} \geq 0 \to x^{2} \leq 9$ $9-x^2>=0 -> x^2 <=9$

$:. f(x)$ is defned for $absx <=3$

Hence the domain of $f(x)$ is $[-3,+3]$

Consider, $0<= sqrt(9-x^2) <= 3$ for $x in [-3,+3]$

$:.f_max = f(abs3) = 5-0 = 5$

and, $f_min = f(0) = 5 -3 =2$

Hence, the range of $f(x)$ is $[2,5]$

We can see these results from the graph of $f(x)$ below.

graph{5-(sqrt(9-x^2)) [-8.006, 7.804, -0.87, 7.03]}

What is the domain and range of y = 5 - (sqrt(9-x^2))y=5−(√9−x2)y = 5 - (sqrt(9-x^2))?