Question

For the function y=ln(x+1)+5, which of the following statements is true?

a. The domain is all real numbers, and the range is [5,∞).

b. The domain is (1,∞), and the range is [5,∞).

c. The domain is (1,∞), and the range is all real numbers.

d. The domain is (-1,∞), and the range is all real numbers.

Answer 1

You cannot take logarithm of a negative number or zero.
Therefore, in y=ln(x+1)+5, (x+1) > 0 or x > -1
The domain is (-1, infinity) (notice it is an open interval on the left).
Log function can take all values from -infinity to +infinity.
So the range is all real numbers.