Question

What is the domain of the function g(x)=3log2(x−1)+4 ? Enter your answer in the box. All real numbers greater than

Answer 1

1

Explanation:

took the test

Answer 2

The domain is
`x>1` (or
`x\in (1,\infty)`), the range is whole real number line (or
`y\in(-\infty,\infty)`).

Explanation:

Consider parent function
`y=\log_2x.` The domain of this function is
`x>0` (or
`x\in(0,\infty)`) and the range of this function is whole real number line (or
`y\in(-\infty,\infty)`).

The function
`g(x)=3\log_2(x-1)+4` can be obtained from the function
`y=\log_2x` by stretch with factor 3 and translation 1 unit to the right and 4 units up. Then the domain of this function becomes
`x>1` (or
`x\in (1,\infty)`) and the range doesn't change.