We need to compute $g(f(x))$, which means substituting $f(x)$ into $g(x)$.

Given functions:

$f(x) = 2x^2 + 3$ $g(x) = \frac{1}{x}$

Step 1: Substitute $f(x)$ into $g(x)$

$g(f(x)) = g(2x^2 + 3)$ Since $g(x) = \frac{1}{x}$, replacing $x$ with $f(x)$ gives: $g(f(x)) = \frac{1}{2x^2 + 3}$

Final Answer:

$g(f(x)) = \frac{1}{2x^2 + 3}$

Would you like a more detailed breakdown of any step?

Here are some related questions to expand on this topic:

1. How do you find $f(g(x))$ instead?
2. What is the domain of $g(f(x))$?
3. How do you determine if $g(f(x))$ is one-to-one?
4. How would the answer change if $g(x) = x^2$ instead?
5. How do you find the inverse of $g(f(x))$?

Tip:

When composing functions, always check the domain of the inner function before substitution.