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:
[tex]f(x)=-\frac{2}{3x}+3[/tex]
a) [tex]f(3)=-\frac{2}{2(3)} +3[/tex]
[tex]=-\frac{1}{3}+3[/tex] [tex]=\frac{-1+6}{3}[/tex] [tex]=\frac{5}{3}[/tex]
b) [tex]f(x)=-5[/tex]
[tex]-5=-\frac{2}{3x}+3[/tex]
[tex]-8=-\frac{2}{3x}[/tex]
[tex]-24x=-2[/tex]
[tex]x=\frac{1}{12}[/tex]
[tex]g(x)=2x-5[/tex]
c) [tex]g(-3)=2(-3)-5[/tex]
[tex]=-6-5[/tex]
[tex]=-11[/tex]
d) [tex]g(x)=-7[/tex]
[tex]-7=2x-5[/tex]
[tex]-2=2x[/tex]
[tex]x=-1[/tex]
e) [tex]g(x)=8[/tex]
[tex]8=2x-5[/tex]
[tex]12=2x[/tex]
[tex]x=6[/tex]
f) [tex]g(x)=9[/tex]
[tex]9=2x-5[/tex]
[tex]11=2x[/tex]
[tex]x=\frac{11}{2}[/tex]