[tex]\boxed{(f \circ g)(7)=199}[/tex]Explanation:In this case, we have the following functions:[tex]f(x)=4x-1 \\ \\ g(x)=x^2+1 \\ \\[/tex]So we need to find:[tex](f \circ g)(7)[/tex]Which is the image of the composition of the function [tex]f[/tex] with [tex]g[/tex] at [tex]x=7[/tex]The Composition of Functions states:[tex]The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f[/tex]The domain of both [tex]f \ and \ g[/tex] is the set of all real numbers. So computing [tex](f \circ g)(x)[/tex]:[tex](f \circ g)(x)=4(x^2+1)-1 \\ \\ \\ Distributive \ Property: \\ \\ (f \circ g)(x)=4x^2+4-1 \\ \\ \\ Simplifying: \\ \\ (f \circ g)(x)=4x^2+3 \\ \\ \\ When \ x =7: \\ \\ (f \circ g)(7)=4(7)^2+3 \\ \\ (f \circ g)(7)=4(49)+3 \\ \\ \boxed{(f \circ g)(7)=199}[/tex]Learn more:Transformation of functions: