To solve $(hg)(2)$, we start by finding $g(2)$ and then use that result to find $h(g(2))$.

Given functions:

• $f(x) = x^2 + 8x - 1$
• $g(x) = -4x + 3$
• $h(x) = 7 - 3x$

Step 1: Find $g(2)$

$g(x) = -4x + 3$ Substituting $x = 2$: $g(2) = -4(2) + 3 = -8 + 3 = -5$

Step 2: Find $h(g(2)) = h(-5)$

$h(x) = 7 - 3x$ Substituting $x = -5$: $h(-5) = 7 - 3(-5) = 7 + 15 = 22$

Therefore, $(hg)(2) = 22$.

Final Answer

$(hg)(2) = 22$

Would you like further details or explanations?

Related Questions:

1. What is $(fh)(2)$ if $f(x) = x^2 + 8x - 1$ and $h(x) = 7 - 3x$?
2. How would you find $h(f(1))$?
3. What are the intercepts of the function $g(x) = -4x + 3$?
4. How do you determine the composition $(gf)(x)$?
5. What is the value of $(fg)(3)$?

Tip

Always work step-by-step, starting with inner functions in compositions to avoid errors.