Question

1) Find f(g(2)) write your answer in simplified fraction.2) Find g(f(2)).

Answer 1

Part 1) Recall that to evaluate a function at a given value, we substitute the variable with the given value.

Then:

`f(g(2))=5g(2)+3.`

Now, evaluating g(x) at x=2 we get:

`g(2)=(2+4)/(2).`

Simplifying the above result we get:

`\begin{gathered} g(2)=(6)/(2), \\ g(2)=3. \end{gathered}`

Substituting the above result in the first equation we get:

`f(g(2))=5*3+3.`

Simplifying the above result we get:

`\begin{gathered} f(g(2))=15+3, \\ f(g(2))=18. \end{gathered}`

Answer Part 1:

`f(g(2))=18.`

Part 2) Analogously to part1 we get that:

`g(f(2))=(f(2)+4)/(2).`

Evaluating f(x) at x=2 we get:

`f(2)=5*2+3.`

Simplifying the above result we get:

`\begin{gathered} f(2)=10+3, \\ f(2)=13. \end{gathered}`

Then:

`g(f(2))=(13+4)/(2).`

Simplifying the above result we get:

`g(f(2))=(17)/(2).`

Answer Part2:

`g(f(2))=(17)/(2).`