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

Given function is:

 

Domain of f:

f (x) is defined if –

Range of f:

Now x assumes real values for all y except (1 – 2y) = 0

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domain= x lies from minus infinity to plus infinity

range= all real values

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We will check for what value the denominator is equal to 0.

Let, 2x+1=0 =>  x = -1/2

Hence, the dom( f(x) ) = R - {-1/2}

and Range = R

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