Solve both parts and justify the conditions used. Part A: Give the real domain and range. Part B: Evaluate the function at the stated input.

1. Part A reasoning

2. Identify the exponent, its real domain and how it changes order.

3. Calculate or simplify this relation.

   $$x^{-2}=1/x^2>0\quad(x\ne0)$$

4. Calculate or simplify this relation.

   $$y>0\Rightarrow x=1/\sqrt y\ne0,\quad f(x)=y$$

5. Every positive output is attained by the displayed nonzero input; zero is excluded as both input and output.

6. Part B reasoning

7. Identify the input domain, rule and requested output before substituting.

8. Calculate or simplify this relation.

   $$f(8)=(8)^2-7(8)+1=9$$

9. Function evaluation is different from solving f(x)=0.

A: Domain: x≠0; range: y>0. B: The requested value is 9.

Checks and common pitfalls: Every positive output is attained by the displayed nonzero input; zero is excluded as both input and output. Function evaluation is different from solving f(x)=0.