Question

Find the domains of the function
√25-9x²​

Answer 1

Answer:

√25-9x²

if we remove root than

5-3x

Answer 2

Answer :

[-5/3 , -5/3]

Solution :

Let the given function be f(x) .

Thus ,

f(x) = √(25 - 9x²)

The given function f(x) to be a real valued function , (25 - 9x²) ≥ 0

=> -(-25 + 9x²) ≥ 0

=> -(9x² - 25) ≥ 0

=> 9x² - 25 ≤ 0 [°•° If a ≥ b then -a ≤ -b]

=> (3x)² - 5² ≤ 0

=> (3x + 5)(3x - 5) ≤ 0

Here ,

Two cases arises :

1) 3x + 5 ≥ 0 and 3x - 5 ≤ 0

OR

2) 3x + 5 ≤ 0 and 3x - 5 ≥ 0

• Case1 : 3x + 5 ≥ 0 and 3x - 5 ≤ 0

=> 3x ≥ -5 and 3x ≤ 5

=> x ≥ -5/3 and x ≤ 5/3

=> -5/3 ≤ x ≤ 5/3

=> x € [-5/3 , -5/3]

OR

• Case2 : 3x + 5 ≤ 0 and 3x - 5 ≥ 0

=> 3x ≤ -5 and 3x ≥ 5

=> x ≤ -5/3 and x ≥ 5/3

=> x € ∅

Hence ,

→ Domain (f) = [-5/3 , -5/3] U ∅

→ Domain (f) = [-5/3 , -5/3]