Final answer:
The function g(x) = x⁶ - 64x⁴ + x² - 7x - 51 was evaluated at x=8, resulting in g(8) = -43 after substituting the value and simplifying the expression.
Step-by-step explanation:
The student asked to evaluate the function g(x) = x⁶ - 64x⁴ + x² - 7x - 51 for the given value of x, which is 8. To do this, we substitute x=8 into the function and calculate the result.
g(8) = (8)⁶ - 64(8)⁴ + (8)² - 7(8) - 51
We calculate each term separately:
- (8)⁶ = 262144
- 64(8)⁴ = 64 * 4096 = 262144
- (8)² = 64
- 7(8) = 56
- And we have the constant -51
Now, plug these values into the equation:
g(8) = 262144 - 262144 + 64 - 56 - 51
After simplifying, we get:
g(8) = 0 + 64 - 56 - 51
g(8) = 64 - 56 - 51
g(8) = 8 - 51
g(8) = -43
Therefore, the value of the function g(8) is -43.