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Answer :
Final answer:
The value of f(-x) - f(x) for the function f(x) = x^3 + x + 7 should be -2x^3 - 2x. The correct answer is e) -2x^3 - 2x.
Explanation:
The value of f(-x) - f(x) for the function f(x) = x^3 + x + 7 is found by substituting -x into the function, then subtracting f(x) from the result. First, we calculate f(-x):
f(-x) = (-x)^3 + (-x) + 7 = -x^3 - x + 7
Now, we subtract f(x) from f(-x):
f(-x) - f(x) = (-x^3 - x + 7) - (x^3 + x + 7)
This simplifies to:
f(-x) - f(x) = -x^3 - x + 7 - x^3 - x - 7
Which further simplifies to:
f(-x) - f(x) = -2x^3 - 2x
The correct answer based on the function f(x) = x^3 + x + 7 should be e) -2x^3 - 2x.
The incomplete question:
What is the value of f(-x) - f(x) for the function f(x) = x³+ x + 7?
a) -2x³ - 7
b) 0
c) 2x³ + 7
d) 2x³ + 2x + 14
e) -2x^3 - 2x.
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