Question

What is the domain of the function g(x)=3log2(x−1)+4 ? All real numbers greater than ___

Answer 1

Answer:

All real numbers greater than 1

Step-by-step explanation:

The domain of a function is the set of possible values in which we can evaluate the function. In other words, it is the possible set of values for x in the expression of the function.

The function is :

$g(x)=3log2(x-1)+4$

The only restriction in the domain of the function g(x) is given by the logarithm in the function.

The argument of the logarithm function must be greater than 0.

Given a logarithm function $log_{a}b=c$ the expression b is called the argument ⇒ In this exercise we need

$2(x-1)>0$

$(x-1)>0$

$x>1$

There isn't another restriction for the logarithm inside g(x) ⇒

The domain of g(x) is all real numbers greater than 1.

Answer 2

Answer-

The domain of $g(x)=3\log 2(x-1)+4$ is,

$\boxed{\boxed{(x:x\ \epsilon\ R\ and\ R>1)}}$

Solution-

For $y=\log x$, there can not have a log to any value of x, which is either negative or 0.

So domain of log x is,

$(x:x\ \epsilon\ R\ and\ R>0)$

Equating 2(x-1) to 0, we can get the domain of the given function, hence

$\Rightarrow 2(x-1)>0\\\\\Rightarrow x-1>0\\\\\Rightarrow x>1$

Therefore, domain of g(x) is any real number greater than 1, i.e

$(x:x\ \epsilon\ R\ and\ R>1)$