Let f(x)=4x-1 and g(x)=x2+1 Find (f•g)(7)

Mathematics

1 answer:

qaws [65]3 years ago

8 0

$\boxed{(f \circ g)(7)=199}$

<h2>Explanation:</h2>

In this case, we have the following functions:

$f(x)=4x-1 \\ \\ g(x)=x^2+1 \\ \\$

So we need to find:

$(f \circ g)(7)$

Which is the image of the composition of the function $f$ with $g$ at $x=7$

The Composition of Functions states:

$The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f$

The domain of both $f \ and \ g$ is the set of all real numbers. So computing $(f \circ g)(x)$ :

$(f \circ g)(x)=4(x^2+1)-1 \\ \\ \\ Distributive \ Property: \\ \\ (f \circ g)(x)=4x^2+4-1 \\ \\ \\ Simplifying: \\ \\ (f \circ g)(x)=4x^2+3 \\ \\ \\ When \ x =7: \\ \\ (f \circ g)(7)=4(7)^2+3 \\ \\ (f \circ g)(7)=4(49)+3 \\ \\ \boxed{(f \circ g)(7)=199}$