What is the domain of f(x)=(3x-8)/(4x+20)

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

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The domain of a function is the set of all possible inputs. Generally, a function has as its domain all real numbers unless the function: takes a root of even index, is a rational function (and thus might have inputs that cause a division by zero), or has a logarithm.

 There are other possible restrictions.

In the case of `f(x)=(3x-8)/(4x+20)` , f(x) is a rational function. Rational functions are defined everywhere except where an input causes a division by zero. This occurs in this function if x=-5. Typically, in order to find restrictions on the domain of rational functions, we set the denominator equal to zero.

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The domain of the function is all real numbers except -5. This can also be written as `RR-{-5},x != -5,(-oo,-5)uu(-5,oo)`

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pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

Let first understand about function f.

It is important to know what type of function f is i.e  f is real function or complex function. If complex then domain will differnt than what domain for real function.

Let f be real function.

`f(x)=(3x-8)/(4x+20)`

f(x) is real as long as `4x+20 !=0`

`4x !=-20`

`x!=-20/4=-5`

`` So f is defined for all real nos. except `x!=-5`

So domain of f is all real nos. except `x!=-5`

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