Question 3
Given: $f(x)=x^{2}-1$ and $g(x)=x-5$
Find: $(f \circ g)(4 b)$
There is no correct answer given.
$8 b^{2}+22 b+56$
$4 b^{2}+36 b+16$
$16 b^{2}-40 b+24$
$12 b^{2}-56 b-18$

Step 1 ：The question is asking for the composition of two functions, $f$ and $g$, evaluated at $4b$. The composition of functions is a concept in mathematics where you apply one function to the result of another function. In this case, we are asked to find $(f \circ g)(4b)$, which means we first apply the function $g$ to $4b$, and then apply the function $f$ to the result.

Step 2 ：To solve this, we first need to find $g(4b)$, then substitute this result into $f(x)$.

Step 3 ：We have calculated the composition of the functions $f$ and $g$ at $4b$. The result is $(4b - 5)^2 - 1$. This is a quadratic expression in terms of $b$.

Step 4 ：Now, we need to simplify this expression to match one of the given options.

Step 5 ：We have simplified the expression to $16b^2 - 40b + 24$. This matches one of the given options, so this is the final answer.

Step 6 ：Final Answer: \(\boxed{16b^2 - 40b + 24}\)