To find $(f \circ g)(x)$, we need to compute $f(g(x))$, which means substituting the function $g(x)$ into the function $f(x)$.

Given:

• $f(x) = 4x + 3$
• $g(x) = 2x^2 + 5x$

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

$(f \circ g)(x) = f(g(x)) = 4(g(x)) + 3$

Substitute $g(x) = 2x^2 + 5x$ into this expression:

$(f \circ g)(x) = 4(2x^2 + 5x) + 3$

Now, distribute the 4:

$(f \circ g)(x) = 8x^2 + 20x + 3$

So, the composition $(f \circ g)(x) = 8x^2 + 20x + 3$.

Would you like more details or have any questions?

Related Questions:

1. What is the reverse composition $(g \circ f)(x)$?
2. How would the result change if $f(x) = 2x + 1$ instead of $f(x) = 4x + 3$?
3. What is the domain of the function $(f \circ g)(x)$?
4. How can you graph the function $(f \circ g)(x)$?
5. How do you find the composition of functions when both functions are quadratic?

Tip:

Always carefully substitute the inner function (like $g(x)$) into the outer function (like $f(x)$) when dealing with compositions!