We are tasked with evaluating $(h - 2f)(5)$ given the functions:

• $h(x) = x^2 - 1$
• $f(x) = -x + 1$.

Let’s solve step by step:

Step 1: Expand $(h - 2f)(x)$

We know: $(h - 2f)(x) = h(x) - 2f(x).$

Step 2: Plug in $x = 5$

We need to evaluate: $(h - 2f)(5) = h(5) - 2f(5).$

Step 3: Calculate $h(5)$

Substitute $x = 5$ into $h(x) = x^2 - 1$: $h(5) = 5^2 - 1 = 25 - 1 = 24.$

Step 4: Calculate $f(5)$

Substitute $x = 5$ into $f(x) = -x + 1$: $f(5) = -(5) + 1 = -5 + 1 = -4.$

Step 5: Calculate $2f(5)$

Multiply $f(5)$ by 2: $2f(5) = 2(-4) = -8.$

Step 6: Combine results

Now substitute into $(h - 2f)(5) = h(5) - 2f(5)$: $(h - 2f)(5) = 24 - (-8) = 24 + 8 = 32.$

Final Answer:

$(h - 2f)(5) = 32.$

Would you like a breakdown of any step? Let me know!

Here are 5 related questions for further practice:

1. If $g(x) = 2x - 3$, what is $(h + g)(2)$?
2. Evaluate $(h \cdot f)(3)$ for the same functions $h(x)$ and $f(x)$.
3. Find $(f - h)(x)$ in terms of $x$ (as a new function).
4. Solve for $x$ if $h(x) = f(x)$.
5. Calculate $(2h + 3f)(4)$.

Tip: Always simplify expressions before substituting values—it saves time and reduces errors!