We are tasked with calculating $f(x) = 2^x - 2$ for $x = 6$ and $x = 8$.

Step 1: Substitute $x = 6$ into the function

$f(6) = 2^6 - 2$ $2^6 = 64, \quad \text{so:} \quad f(6) = 64 - 2 = 62$

Step 2: Substitute $x = 8$ into the function

$f(8) = 2^8 - 2$ $2^8 = 256, \quad \text{so:} \quad f(8) = 256 - 2 = 254$

Final Results:

$f(6) = 62$ $f(8) = 254$

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Related Questions:

1. What are the values of $f(x)$ for $x = 4$ and $x = 7$?
2. What is the graph of $f(x) = 2^x - 2$ in the range $0 \leq x \leq 10$?
3. How does $f(x) = 2^x - 2$ behave as $x \to \infty$?
4. Can $f(x) = 2^x - 2$ ever equal zero? Solve for $x$ if yes.
5. What is the derivative of $f(x) = 2^x - 2$, and what does it tell us about the function's growth?

Tip: Memorize powers of 2 up to $2^{10}$ for quick calculations in exponential functions.