Answer

Verified

385.8k+ views

**Hint:**For the domain we have to find the value of $x$ for which the given function is always defined , in this case we will put the value under root greater than equal to zero, and then find the values of $x$ which it is defined.

**Complete step-by-step solution:**

Given: Let the function be, $f(x) = \sqrt {x + 7} $

To find: We have to find the domain of the given function $f(x) = \sqrt {x + 7} $

Given real function is $f(x) = \sqrt {x + 7} $

As we know if the value of the square root is negative then the function is not defined.

So the value of the square root is always greater than or equal to zero.

Thus $f(x) = \sqrt {x + 7} \geqslant 0$………………….$(1)$

Now squaring both sides, we have

$(x + 7) \geqslant 0$

On rewriting we get,

$x \geqslant - 7$

Therefore the domain of $f$ is the set of all the numbers which are greater than or equal to $ - 7$

That is the domain of the $f(x)$ is $[ - 7,\infty )$ (Where domain is greater than or equal to $ - 7$ so at $ - 7$ there is a closed interval and at infinity there is an open interval).

Now from the equation $(1)$

$\sqrt {x + 7} \geqslant 0$

But $f(x) = \sqrt {x + 7} $

$ \Rightarrow f(x) \geqslant 0$

Therefore the domain of $f$ is the set of real numbers greater than or equal to $0$ (zero).

That is the domain of $f = [ - 7,\infty )$(domain is greater than or equal to $0$ (zero) so at $ - 7$ there is a closed interval and at infinity there is an open interval).

Hence, this is the required answer.

**Note:**Domain is an independent set of those values for a given function which on substitution always gives values of result.

Solutions of inequalities are always written in the form of intervals like close and open intervals.

Recently Updated Pages

Find the value of cos 260 circ sin 230 circ + tan 230 class 10 maths CBSE

How do you identify dfrac1cot2x + 1 class 10 maths CBSE

Evaluate the following sin 30circ cos 30circ class 10 maths CBSE

What will be the area of the triangle formed by the class 10 maths CBSE

Find the missing number in the pattern 2581117202326 class 10 maths CBSE

What is the standard form of y left 2x 3 right2 class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail

Name 10 Living and Non living things class 9 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths