Question

What are the domain and range of f(x)=log(x-1)+2?

Answer 1

The correct answer on edgen. is

B) domain: x > 1; range: all real numbers

Answer 2

Answer: Domain = $(-1, \infty)$

Range = $(-\infty, \infty)$

Step-by-step explanation:

Here, the given function,

$f(x) = log(x-1) + 2$

Since log( negative number ) = not defined

Also,

$log(0) = -\infty$

Hence, f(x) is defined if x - 1 > 0

⇒ x > 1

Thus, f(x) is defined for all the values that are greater than 1,

⇒ Domain of f(x) = All real number greater than 1,

= $(1, \infty)$

Now, for the interval $(1, \infty)$,

f(x) can be any real number.

Thus, the range of the given function = $(-\infty, \infty)$