Question

Find the domain and range of f(x)= root 25-x^2

Answer 1

Given
f(x) = √(25 - x²)
for defining function,
25 - x² ≥ 0
(5 - x)(5 + x) ≥ 0
-5 ≤ x ≤ 5
hence, domain €[ -5 , 5 ]

now,
y = √(25 - x²)
differentiate with respect to x
dy/dx = 1/2√(25 - x²) × (-2x)
dy/dx = -x/√(25 - x²)
hence,
for x < 0 function is increasing and x > function is decreasing .

hence,
f(-5) = 0
f(0) = 5
f(5) = 0

range € [ minimum value of f(x), maximum value of f(x)]
range€ [ 0, 5]

Answer 2

Answer:

f(x) = √(25 - x²)

for defining function,

25 - x² ≥ 0

(5 - x)(5 + x) ≥ 0

-5 ≤ x ≤ 5

hence, domain €[ -5 , 5 ]

now,

y = √(25 - x²)

differentiate with respect to x

dy/dx = 1/2√(25 - x²) × (-2x)

dy/dx = -x/√(25 - x²)

hence,

for x < 0 function is increasing and x > function is decreasing .

hence,

f(-5) = 0

f(0) = 5

f(5) = 0

range € [ minimum value of f(x), maximum value of f(x)]

range€ [ 0, 5]

Step-by-step explanation: