Question

what is the domain of the following question
$\sqrt{25 - {x}^{2} }$
​

Answer 1

Answer❣

Solution

=>8x²-14x-9=0

The above equation is in the form of a quadratic equation so,we simply factorise it by middle term splitting method.

Step by step explanation:

How to factorise..??

8x²-14x-9=0

The coefficient of x² is 8

-14x is a middle term and its coefficient is 14.

and the constant" is +3

Step-1 : Multiply the coefficient of x² by the constant -9×8= -72

Step-2 : Find two factors of 72 whose sum is equal to the coefficient of the middle term, which is -14.

=>8x²-14x-9=0

-9×8= -72

-72 = -18× 4

and -18+4= -14

=>8x²-14x-9=0

=>8x²-18x+4x-9=0

=>2x(4x-9)+1(4x-9)=0

=>(2x+1)(4x-9)=0

=>2x+1=0

=>2x= -1

=>x= -1/2

(4x-9)=0

=>4x=9

=>x=9/4

∴ x = -1/2 & x = 9/4

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Answer 2

Answer:

The domain is   =  [  − 5 ,  5 ]

Step-by-step explanation:

f(x) = √(25 - x²)

for defining a function,

25 - x² ≥ 0

(5 - x)(5 + x) ≥ 0

-5 ≤ x ≤ 5

Hence, domain €[ -5, 5]