Question

1-25. Given f(x) =- 2/3x +3 and g(x) = 2x2 - 5, complete parts (a) through (f).

Answer 1

Answer:

When f or g are equivalent to a number you are solving for x. For example b, d, e, f. In the equation g(x) =2x2-5 I assumed 2 was a typo. So, if it's incorrect, please use same steps and just adjust the solution.

Step-by-step explanation:

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

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

           $=-\frac{1}{3}+3$ $=\frac{-1+6}{3}$ $=\frac{5}{3}$

b) $f(x)=-5$

      $-5=-\frac{2}{3x}+3$

      $-8=-\frac{2}{3x}$

  $-24x=-2$

        $x=\frac{1}{12}$

$g(x)=2x-5$

c) $g(-3)=2(-3)-5$

               $=-6-5$

               $=-11$

d) $g(x)=-7$

      $-7=2x-5$

      $-2=2x$

        $x=-1$

e) $g(x)=8$

        $8=2x-5$

       $12=2x$

        $x=6$

f)  $g(x)=9$

         $9=2x-5$

        $11=2x$

         $x=\frac{11}{2}$