Question

I need help with somr questions

Answer 1

To solve the exercise, first we are going to write the composition of the functions:

`\begin{gathered} \text{ Given two functions }f(x)\text{ and }g(x)\colon \\ f\lbrack g(x)\rbrack=(f\circ g)(x) \end{gathered}`

It reads "f composed of g", simply said "we are going to fill f with g":

So, in this case, we have

`\begin{gathered} f(x)=(48)/(x^2)-(12)/(x)+1 \\ g(x)=2x \\ f\lbrack g(x)\rbrack=(48)/((2x)^2)-(12)/(2x)+1 \\ f\lbrack g(x)\rbrack=(48)/(4x^2)-(12)/(2x)+1 \\ \text{ Simplifying} \\ f\lbrack g(x)\rbrack=(12)/(x^2)-(6)/(x)+1 \end{gathered}`

Now, we evaluate, that is, we replace x = 2 in the composite function and operate

`\begin{gathered} f\lbrack g(2)\rbrack=(12)/((-2)^2)-(6)/(-2)+1 \\ f\lbrack g(2)\rbrack=(12)/(4)+3+1 \\ f\lbrack g(2)\rbrack=3+3+1 \end{gathered}`

Therefore,

`f\lbrack g(2)\rbrack=7`