​f(x)equals7minus4x and ​g(x)equals2plusx squared  (gcircle​g)(x)equals

To compute \((g \circ g)(x)\), this means we need to apply the function \(g(x)\) to itself, i.e., substitute \(g(x)\) into the \(g(x)\) function.

Given:
- \(g(x) = 2 + x^2\),

To find \((g \circ g)(x)\), we substitute \(g(x)\) into itself:
\[
(g \circ g)(x) = g(g(x)) = g(2 + x^2)
\]

Now, substitute \(2 + x^2\) into \(g(x)\):
\[
g(2 + x^2) = 2 + (2 + x^2)^2
\]

Now expand \((2 + x^2)^2\):
\[
(2 + x^2)^2 = (2 + x^2)(2 + x^2) = 4 + 4x^2 + x^4
\]

So:
\[
g(2 + x^2) = 2 + 4 + 4x^2 + x^4 = 6 + 4x^2 + x^4
\]

Thus, \((g \circ g)(x) = x^4 + 4x^2 + 6\).

Would you like more details on this or have any questions?

Here are 5 related questions:
1. What would \((f \circ g)(x)\) be?
2. What is \((g \circ f)(x)\)?
3. How do we differentiate composite functions like \((g \circ g)(x)\)?
4. Can you compute \((f \circ f)(x)\)?
5. How does substitution work in function composition?

**Tip:** Always start by simplifying the inner function first when working with composite functions.

f(x) equals 7 minus 4x and g(x) equals 2 plus x squared. What is (g ∘ g)(x)?

Learn how to solve (g ∘ g)(x) where g(x) = 2 + x^2. This solution involves key concepts such as function composition, substitution, and polynomial expansion. Perfect for high school students (Grades 9-12).

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