Concept
Substitute x = 5 in all the function, your answer will be the function whose f(5) = 38.
Option A
Substitute x = 5 in the option A
[tex]\begin{gathered} f(x)\text{ = (}\frac{-8}{5})x^2\text{ + 4x + 5} \\ f(5)\text{ = (}\frac{-8}{5}\text{) }\times5^2\text{ + 4(5) + 5} \\ =\text{ }\frac{-8\text{ x 25}}{5}\text{ + 20 + 5} \\ =\text{ -40 + 25} \\ =\text{ -15} \\ \text{Hence option A is wrong} \end{gathered}[/tex]Option B
[tex]\begin{gathered} f(x)\text{ = -2}x^2\text{ + (}\frac{8}{5}\text{)x + 14} \\ f(5)\text{ = -2 }\times5^2\text{ + }\frac{8\text{ x 5}}{5}\text{ + 14} \\ =\text{ -50 + 8 + 14} \\ =\text{ -28} \\ \text{Option B is wrong} \end{gathered}[/tex]Option C
[tex]\begin{gathered} f(x)\text{ = (}\frac{4}{5})x^2\text{ + 4x - 2} \\ f(5)\text{ = (}\frac{4}{5}\text{) }\times5^2\text{ + 4(5) - 2} \\ =\text{ 20 + 20 - 2} \\ =\text{ 38} \\ \text{Option C is the correct answer} \end{gathered}[/tex]Final answer: Option C
