Question

find the domain and range of f(x)=x-3/2x+1

please show steps

Answer 1

Answer:

Range = R

Domain = R - { -1/2 }

Step-by-step explanation:

2x + 1 = 0

2x = -1

x = - 1 / 2

Therefore ,

Domain = R - { -1/2 }

All real numbers are used as range here. For getting solve the denominator of the given fraction and reduce the value of x from the real number "R".

Hope it helps you dude . If so please tag me as brainliest.

Have a great day.

Answer 2

Answer:

The range of f(x) is (-∞, ∞) - {1/2}.

the domain of f(x) is (-∞, ∞) - {-1/2}.

Step-by-step explanation:

Given,

The function:

$f(x) = \frac{x-3}{2x+1 }$

To find,

The domain and range of f(x)

Step (1): Finding the domain

The function

$f(x) = \frac{x-3}{2x+1 }$ is not defined at:

2x+1 = 0

i.e. $x = \frac{-1}{2}$ is the only point where the function f(x) is not defined

therefore, domain of f(x) is (-∞, ∞) - {-1/2}

Step (2): Finding the range

Let f(x) = y

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

Now, finding where the function x is not defined

i.e. when 1 - 2y = 0

⇒ y = 1/2 is the only point where the function f(x) is not defined.

Therefore, the range of f(x) is (-∞, ∞) - {1/2}.

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