Find the domain and the range of each of the following real

Question:

Find the domain and the range of each of the following real

function: $f(x)=\sqrt{3 x-5}$

 

Solution:

Given: $f(x)=\sqrt{3 x-5}$

Need to find: Where the functions are defined.

The condition for the function to be defined,

$3 x-5 \geq 0$

$\Rightarrow x \geq \frac{5}{3}$

So, the domain of the function is the set of all the real numbers greater than equals to $\frac{5}{3}$.

The domain of the function, $\mathrm{D}_{\mathrm{f}(\mathrm{x})}=\left[\frac{5}{3}, \infty\right)$.

Putting $\frac{5}{3}$ in the function we get, $f(x)=0$

It means the range of the function is defined for all the values greater than equals to 0.

The range of the function, $\operatorname{R}_{\mathrm{f}(\mathrm{x})}=[0, \infty)$.

 

 

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