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

1.	Find the domain and the range of each of the following real function: f(x) = \(\frac{1}{\sqrt{2x-3}}\)
Answer» Given: f(x) = \(\frac{1}{\sqrt{2x-3}}\) Need to find: Where the functions are defined. 2x - 3 > 0 ⇒ x > \(\frac{3}2\) So, the domain of the function is the set of all the real numbers greater than \(\frac{3}2\). The domain of the function, D_f(x) = (\(\frac{3}2\),∞). Now putting any value of x within the domain set we get the value of the function always a fraction whose denominator is not equals to 0. The range of the function, R_f(x) = (0, 1).

Find the domain and the range of each of the following real function: f(x) = \(\frac{1}{\sqrt{2x-3}}\)

Answer»

Given: f(x) = \(\frac{1}{\sqrt{2x-3}}\)

Need to find: Where the functions are defined.

2x - 3 > 0

⇒ x > \(\frac{3}2\)

So, the domain of the function is the set of all the real numbers greater than \(\frac{3}2\).

The domain of the function, D_f(x) = (\(\frac{3}2\),∞).

Now putting any value of x within the domain set we get the value of the function always a fraction whose denominator is not equals to 0.

The range of the function, R_f(x) = (0, 1).