Question

Find the domain and range of the given real function f(x) =√49-x2

Answer 1

Answer:

Set the denominator in 49x2−49 49 x 2 - 49 equal to 0 0 to find where the expression is undefined. x2−49=0 x 2 - 49 = 0. Solve for x x .

Step-by-step explanation:

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Answer 2

Answer:

Range : x ∈ [ -7, 7 ]

Domain : y ∈ [ 0,7 ] .

Step-by-step explanation:

Given :- $f(x) = \sqrt{49-x^2 }$

To find :-

• Range and domain of f(x)

Solution :-

Step 1) function is $f(x) = \sqrt{49-x^2 }$ -- (1)

Step 2) For range ,

$f(x) = \sqrt{49-x^2}$

since , square root is always (+)ve. i.e. ≥ 0

therefore , $\sqrt{49-x^2} \geq 0\\49-x^2 \geq 0 \\x^2\leq 49\\x\leq 7 , -7$

thus , x ∈ [ -7,7 ] --- (2)

Step 3) For Domain ,

let , f(x) = y = $\sqrt{49-x^2}$ --- (2)

thus , $y^2 = 49-x^2 \\x^2= 49-y^2$ ---- (3)

$x = \sqrt{49-y^2}$

Square root is always (+)ve ≥ 0 ,

thus ,

$\sqrt{49-y^2} \geq 0\\49-y^2\geq 0\\y^2\leq 49\\y\leq -7,7$

domain is always (+)ve.

Thus domain of f(x) is y ∈ [ 0,7 ] .

Hence ,

Range : x ∈ [ -7, 7 ]

Domain : y ∈ [ 0,7 ]

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