Answer
Verified
430.2k+ views
Hint: In this question we have to find the value $x$ where the function given in the question is defined. We all know that logarithm is defined only for the value of $x$ which is greater than $1$ . Therefore, we will put the variable part of the function given in the question greater than $1$ to find the domain of the function. The domain of the function is the value of $x$ where the function is defined.
Complete step-by-step solution:
The given function is $f\left( x \right) = \log \left( {x - 5} \right)$ .
For a function if we have to find the domain then find the value of $x$ where that particular function is defined
Now, to find the domain of the function we will put the variable part of the function greater than $1$ . Therefore, we can write:
$
x - 5 > 0 \\
\Rightarrow x > 5
$
Now, from the above we can write $x \in \left( {5,\infty } \right)$ . Therefore, the domain of $\log \left( {x - 5} \right)$ is $\left( {5,\infty } \right)$ .
Hence, the correct option is (A).
Note: The domain of a logarithmic function is greater than $1$ and the range of the logarithmic function is the set of real numbers. For a function if we have to find the range then find the value of $y$ the function can take.
The important thing in this question is that we should have an idea about the value of $x$ where $\log $ is defined. Because if we don’t know that we will not be able to start the question. And be careful about whether to put an open bracket or close bracket on the values of $x$ because it will lead to incorrect answers.
Complete step-by-step solution:
The given function is $f\left( x \right) = \log \left( {x - 5} \right)$ .
For a function if we have to find the domain then find the value of $x$ where that particular function is defined
Now, to find the domain of the function we will put the variable part of the function greater than $1$ . Therefore, we can write:
$
x - 5 > 0 \\
\Rightarrow x > 5
$
Now, from the above we can write $x \in \left( {5,\infty } \right)$ . Therefore, the domain of $\log \left( {x - 5} \right)$ is $\left( {5,\infty } \right)$ .
Hence, the correct option is (A).
Note: The domain of a logarithmic function is greater than $1$ and the range of the logarithmic function is the set of real numbers. For a function if we have to find the range then find the value of $y$ the function can take.
The important thing in this question is that we should have an idea about the value of $x$ where $\log $ is defined. Because if we don’t know that we will not be able to start the question. And be careful about whether to put an open bracket or close bracket on the values of $x$ because it will lead to incorrect answers.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE