Question

what is the domain and range of this function f(x) = log5(x-2)+1

Answer 1

Hello! The answer would be

X-2>0

x>2

log (5)( x-2)

it can be any real number and that would be the range

Answer 2

The domain of the given function f(x) is all the real numbers grater than 2 and the range of the given function f(x) is all the real numbers.

What is the domain of the function?

The domain of a function is the set of values that we are allowed to plug into our function.

What is the range of the function?

The set of all output values of a function is called range.

According to the given question.

We have a logarithmic function

$f(x) = log_{5} (x-2)+1$

At x = 2, the above logarithmic function is not defined.

Because $log0$ is undefined.

And the logarithm of negative numbers is undefined.

So, the above function is defined for

$x-2 > 0$

$\implies x > 2$

Therefore, the domain of the above function f(x) is all the real numbers which are greater than 2.

So, if we plug all the real numbers which are greater than 2 in the given function f(x), we get only real numbers.

Therefore, the range of the given function f(x) is all the real numbers.

Hence, the domain of the given function f(x) is all the real numbers grater than 2 and the range of the given function f(x) is all the real numbers.

Find out more information about domain and range of a function here:

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