To find the leading coefficient of the polynomial \( f(x) = 7x - 8x^5 - 2 + 9x^2 + 2x^7 \), we first need to identify the term with the highest degree.
The terms of the polynomial are:
- \( 7x \) (degree 1)
- \( -8x^5 \) (degree 5)
- \( -2 \) (degree 0, constant term)
- \( 9x^2 \) (degree 2)
- \( 2x^7 \) (degree 7)
The term with the highest degree is \( 2x^7 \), which has a degree of 7. The leading coefficient is the coefficient of this term, which is \( 2 \).
Therefore, the leading coefficient of the polynomial \( f(x) \) is \( \boxed{2} \).
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