Evaluate (-5)3 Mathematics
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Answer:
- <em>To solve these first swap x and y, solve for y and name it inverse function</em>
3. <u>y = -8x + 2</u>
- x = -8y + 2
- 8y = -x + 2
- y = -x/8 + 2/8
- y = -(18)x + 1/4
f⁻¹(x) = -(18)x + 1/4
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4.<u> y = (2/3)x - 5</u>
- x = (2/3)y - 5
- (2/3)y = x + 5
- y = (3/2)x + (3/2)5
- y = 1.5x + 7.5
f⁻¹(x) = 1.5x + 7.5
-----------------------------------------
5. <u>f(x) = 2x² - 6</u>
- x = 2y² - 6
- 2y² = x + 6
- y² = 1/2x + 3
- y =
f⁻¹(x) =
-----------------------------------------
6. <u>y = (x - 3)²</u>
- x = (y - 3)²
= y - 3
- y = 3 +
f⁻¹(x) = 3 +
The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.
In fact, if you use complex number, then a polynomial with degree n has exactly n roots.
So, in particular, a third-degree polynomial can have at most 3 roots.
In fact, in general, if the polynomial has solutions
, then you can factor it as
So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as
But this is a fourth-degree polynomial.