Answer:
[tex]f(g(2))=10[/tex]
Step-by-step explanation:
We have the two functions: [tex]f(x)=3x-5[/tex] and [tex]g(x)=2+\frac{6}{x}[/tex].
We want to find [tex]f(g(2))[/tex].
So, let's use the second function to find [tex]g(2)[/tex] first:
[tex]g(2)=2+\frac{6}{2}[/tex]
Divide:
[tex]g(2)=2+3[/tex]
Add:
[tex]g(2)=5[/tex]
Therefore, our expression is the same to [tex]f(g(2))=f(5)[/tex].
Now, we can substitute 5 for f(x). This yields:
[tex]f(5)=3(5)-5[/tex]
Multiply:
[tex]f(5)=15-5[/tex]
Subtract:
[tex]f(5)=10[/tex]
So:
[tex]f(g(2))=10[/tex]
And we're done!
