How do you find the domain and range of f(x) = ln(-x+5)+8

garkochenvz

garkochenvz

Answered question

2022-08-13

How do you find the domain and range of f ( x ) = ln ( x + 5 ) + 8?

Answer & Explanation

Zechariah Zavala

Zechariah Zavala

Beginner2022-08-14Added 14 answers

As we can have logarithm of only a positive number, we must have
-x+5>0 or x<5, which gives the domain.
The least possible value of ln ( x + 5 ) is and its maximum possible value is
Hence, range is ( , )
Lacey Rojas

Lacey Rojas

Beginner2022-08-15Added 2 answers

The function is
f ( x ) = ln ( x + 5 ) + 8
The logarith function ln x is defined for x>0
Therefore,
-x+5>0
x<5
The domain is x ( , 5 )
To find the range, let
y = ln ( x + 5 ) + 8
ln ( 5 x ) = y 8
5 x = e y 8
x = 5 e y 8
The exponential function e x is defined over R
Therefore,
The range is y R
graph{ ln ( 5 x ) + 8 [ 38 , 35.07 , 15.4 , 21.14 ]}

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