To find $(f \circ g)(x)$, also known as the composition of functions $f$ and $g$, you substitute $g(x)$ into $f(x)$. In other words:

$(f \circ g)(x) = f(g(x))$

Given that:

• $f(x) = 7 - 4x$
• $g(x) = 2 + x^2$

Now, substitute $g(x)$ into $f(x)$:

$(f \circ g)(x) = f(g(x)) = f(2 + x^2)$

Substitute $2 + x^2$ into $f(x)$:

$f(2 + x^2) = 7 - 4(2 + x^2)$

Simplify the expression:

$f(2 + x^2) = 7 - 4(2) - 4(x^2)$ $= 7 - 8 - 4x^2$ $= -1 - 4x^2$

Thus, the composition of $f$ and $g$ is:

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

Would you like further details on function composition or any other clarification?

Here are 5 related questions to consider:

1. How would you compute $(g \circ f)(x)$?
2. What happens if $f(x)$ and $g(x)$ are inverse functions?
3. Can you find the domain of $(f \circ g)(x)$?
4. How does function composition affect the range of the resulting function?
5. Can you graph $f(x)$, $g(x)$, and $(f \circ g)(x)$ to visualize the result?

Tip: In function composition, pay careful attention to the order of the functions. $f(g(x))$ is not the same as $g(f(x))$.