Answer:
I am unsure of the wording of this question, so I will answer both ways I see it.
When x = x + 3, the value of 2x³ + x² - x is 2x³ + 19x² + 59x + 66.
When x = 3, the value of 2x³ + x² - x is 60.
Explanation:
x = x + 3 solution:
It is given that:
f(x) = 2x³ + x² - x
We are trying to find this when x = x+3. Substitute this value in for every x in the function.
f(x + 3) = 2(x + 3)³ + (x + 3)² - (x + 3)
Expand the first part.
f(x + 3) = 2(x + 3)(x + 3)(x + 3) + (x + 3)² - (x + 3)
Multiply pairs together.
f(x + 3) = 2(x + 3)(x² + 6x + 9) + (x + 3)² - (x + 3)
Multiply the remaining pairs together.
f(x + 3) = 2(x³ + 9x² + 27x + 27) + (x + 3)² - (x + 3)
Distribute the two inside the parenthesis.
f(x + 3) = 2x³ + 18x² + 54x + 54 + (x + 3)² - (x + 3)
Evaluate (x + 3)².
f(x + 3) = 2x³ + 18x² + 54x + 54 + (x² + 6x + 9) - (x + 3)
Remove all parenthesis and start simplifying.
f(x + 3) = 2x³ + 18x² + 54x + 54 + x² + 6x + 9 - x - 3
Combine all terms ending in x².
f(x + 3) = 2x³ + (18x² + x²) + 54x + 54 + 6x + 9 - x - 3
f(x + 3) = 2x³ + 19x² + 54x + 54 + 6x + 9 - x - 3
Combine all terms ending in x.
f(x + 3) = 2x³ + 19x² + (54x + 6x - x) + 54 + 9 - 3
f(x + 3) = 2x³ + 19x² + 59x + 54 + 9 - 3
Last, combine the final numbers to get:
f(x + 3) = 2x³ + 19x² + 59x + 60
x = 3 solution:
It is given that:
f(x) = 2x³ + x² - x
Substitute 3 in for every value of the function.
f(3) = 2(3)³ + (3)² - 3
Evaluate 3 cubed and then multiply it by 2.
f(3) = 2(27) + 3² - 3
f(3) = 54 + 3² - 3
Evalute 3 squared.
f(3) = 54 + 9 - 3
Add 54 and 9.
f(3) = 63 - 3
Subtract 3 from 63 to get:
f(3) = 60