Question 992558
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Find the domain and range and sketch the graph for the functions f and g where f(x) is given by the polynomial below and g(x)=|f(x)|. 
Also use the graph to solve the inequality f(x)<0. 
f(x)=9+3x-2x^2
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The domain of the function &nbsp;f&nbsp; is the entire number line, &nbsp;i.e. &nbsp;the set of all real numbers. &nbsp;(It is so for any polynomial). 


The domain of the function &nbsp;g&nbsp; is the same entire number line, &nbsp;i.e. the set of all real numbers.

The plots of &nbsp;f&nbsp; and &nbsp;g&nbsp; are shown in the Figure below. &nbsp;The plot of &nbsp;g&nbsp; is in green. &nbsp;Partly it is over-posed the plot of &nbsp;f.

<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -5.5, 5.5, -5.5, 10.5,
          9+3x-2x^2,
          abs(9+3x-2x^2)
)}}}

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  </TR>
</TABLE>

The roots of f are &nbsp;3&nbsp; and &nbsp;{{{-3/2}}}. 

f(x) < 0 &nbsp;in two semi-infinite intervals &nbsp;({{{-infinity}}}, {{{-3/2}}}) &nbsp;and &nbsp;(3, {{{infinity}}}).