[tex]\boxed{(f \circ g)(7)=199}[/tex]
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]
Transformation of functions: https://brainly.com/question/12469649
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