Question

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question------------15,16​

Answer 1

Given : y = √log(x + 1)

y =  log { (x² + 8x + 7)/(x² +  7) }

To Find :   Domain and range

Solution:

y = √log(x + 1)

Square root of negative number not defined

Hence

log(x + 1) ≥ 0

log ( 1) = 0

=> x + 1 ≥ 1

=> x ≥  0

Domain = [0 , ∞ )

Range = [0 , ∞ )

y =  log { (x² + 8x + 7)/(x² +  7) }

log of -ve and 0  not defined

=>  (x² + 8x + 7)/(x² +  7)  >  0

x² +  7  is always +ve

Hence x² + 8x + 7 > 0

=>  (x + 7)(x + 1) > 0

x < - 7  or  x >  - 1

Domain  = (-∞ , - 7) ∪ ( - 1 , ∞)

Domain  =  R - [-7 , - 1]

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Answer 2

Answer:

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