Question

Find the domain and range of the function f(x)=(3x-5)/(2x+5)

Answer 1

I hope it will be answer of your question

Answer 2

Answer:

The domain of the function is

$( - \infin \: ,\frac{ - 5}{2} )U( \frac{ - 5}{2} ,\infin )$

The range if the function is

$( - \infin \: ,\frac{ 3}{2} )U( \frac{ 3}{2} ,\infin )$

Step-by-step explanation:

The given function is

$f(x) = \frac{3x - 5}{2x + 5}$

We are required to find the domain and range of the function

Domain

For the function to exist and be finite,the denominator must not be equal to zero.Therefore,

$= > 2x+5≠0 = > x≠ \frac{ - 5}{2}$

The function exists for all inputs except -2.5.Hence,the domain of the function is

$( - \infin \: ,\frac{ - 5}{2} )U( \frac{ - 5}{2} ,\infin )$

Range

Let the given function be

$y = \frac{3x - 5}{2x + 5}$

$= > y(2x + 5) = 3x - 5 \\ = > 2xy + 5y - 3x = - 5 \\ = > x(2y - 3) = - 5 - 5y \\ = > x = \frac{5(1 + y)}{3 - 2y}$

For x to be finite,the denominator must not be equal to zero

$=>3-2y≠0 \\ =>y≠\frac{3}{2}=>f(x)≠ \frac{3}{2}$

Therefore,the Range of the function is

$( - \infin \: ,\frac{ 3}{2} )U( \frac{ 3}{2} ,\infin )$

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