Evaluating Composition

$( f o g)(x) = f(g(x))$

$g(4) = \frac{8}{5}$

$f(\frac{8}{5}) = 8 + 5 = 13$

We've the values of f(x) & g(x): Now, we got to solve $f o g (4)$ , If we simplify this term a li'l bit, we get: $f(g(x))$ where x=4 .

First Step: Solve the g(x) for x=4 : $\frac{4 \times 4}{3 \times 4 - 2} = \frac{8}{5}$

Second Step: solve f(x) for x=8/5 : $5 \times \frac{8}{5} + \frac{6}{2 \times \frac{8}{5} -2}$

on further solving we get: $8+5=13.$

So, our answer is 13.

$g({x})=\frac{4x}{3x-2}$

$g({4})=\frac{4({4})}{3({4})-2}$

which simplifies to $\frac{8}{5}$

$f({x})={5x}+\frac{6}{2x-2}$

$f(\frac{8}{5})={5}(\frac{8}{5})+\frac{6}{2(\frac{8}{5})-2}$

which simplifies to ${8}+{5}$

that gives an answer of $\boxed{13}$

fog(4)=f(g(4))

g(4)=4(4)/(3(4)-2)=8/5

f(8/5)=..... =13

f belongs g so, we need to put all in the function g x f