Question

Please explain in words the meaning of this notation.

(f ° g)(3)

Answer 1

f of g of x
f(g(x))
plug x into g(x) and solve, place that solved value as the input in f(x) and solve for final answer

Answer 2

x in this case is 3 so
solve f(3) 1st

Answer 3

@ehuman is there anything else ??

Answer 4

(f ° g)(3)
means you take the value of 3 in place of x in G(x)
then use that value in place of x and solve f(x)

Answer 5

(f of g(x)) or as the notation goes (fog)(x) is just g(x) as argument of the function f(x)
so f(x) is a HOST function to the CLIENT g(x)

let's say for example, let us use these 2 functions
\(\bf f(x) = x^2+2x-1\qquad \qquad g(x) = \color{red}{5 - x}\\ \quad \\

(fog)(x)= f(\quad g(x)\quad )\implies (\quad \color{red}{g(x)}\quad )^2+2(\quad \color{red}{g(x)}\quad )-1\\ \quad \\

(fog)(3)= f(\quad g(3)\quad )\implies (\quad \color{red}{g(3)}\quad )^2+2(\quad \color{red}{g(3)}\quad )-1\\ \quad \\
\color{blue}{g(3) = 5 - (3)\implies 2}\qquad thus\\ \quad \\
(fog)(3)= f(\quad g(3)\quad )\implies (\quad \color{red}{g(3)}\quad )^2+2(\quad \color{red}{g(3)}\quad )-1\\ \quad \\
\implies (fog)(3)= f(\quad g(3)\quad )\implies (\quad \color{red}{2}\quad )^2+2(\quad \color{red}{2}\quad )-1\)