Let's solve the problems given in the image.

The functions provided are:

• $f(x) = 4x - 5$
• $g(x) = x^2 + 4$

We are asked to compute the following:

a) $(f \circ g)(x)$ or $f(g(x))$

This means we need to substitute $g(x)$ into $f(x)$.

$f(g(x)) = f(x^2 + 4) = 4(x^2 + 4) - 5$ $= 4x^2 + 16 - 5$ $= 4x^2 + 11$

b) $(g \circ f)(x)$ or $g(f(x))$

This means we need to substitute $f(x)$ into $g(x)$.

$g(f(x)) = g(4x - 5) = (4x - 5)^2 + 4$ $= (16x^2 - 40x + 25) + 4$ $= 16x^2 - 40x + 29$

So the answers are:

• $(f \circ g)(x) = 4x^2 + 11$
• $(g \circ f)(x) = 16x^2 - 40x + 29$

Would you like any further details or explanations?

Here are some related questions for practice:

1. What is $(f \circ f)(x)$ if $f(x) = 4x - 5$?
2. What is $(g \circ g)(x)$ if $g(x) = x^2 + 4$?
3. If $f(x) = 2x + 3$ and $g(x) = x^2 - 1$, what is $(f \circ g)(x)$?
4. How would you find $f(x + 1)$ for $f(x) = 4x - 5$?
5. How does the result of $(g \circ f)(x)$ change if $g(x) = x^2 - 4$?

Tip: When dealing with composite functions, always apply the inner function first, then the outer function.