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derivative?
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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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