2 years ago

Given that f(x) x2 + 3x 10 and g(x) = x – 2, find f (x) · g(x) and

Mathematics

1 answer:

lakkis [162]2 years ago

4 0

Answer:

x^3 + x^2 + 4x - 20.

Step-by-step explanation:

I have assumed there is a + between the 3x and the 10.

f(x) * g(x)

= (x^2 + 3x + 10)(x - 2)

= x^3 + 3x^2 + 10x - 2x^2 - 6x - 20

= x^3 + x^2 + 4x - 20.

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Prove the theorem (AB )^T= B^T. A^T

Lisa [10]

Answer:

$(AB)^T = B^T.A^T (Proved)$

Step-by-step explanation:

Given (AB )^T= B^T. A^T;

To prove this expression, we need to apply multiplication law, power law and division law of indices respectively, as shown below.

$(AB)^T = B^T.A^T\\\\Start, from \ Right \ hand \ side\\\\B^T.A^T = \frac{B^T.A^T}{A^T}.\frac{B^T.A^T}{B^T} (multiply \ through) \\\\ = \frac{A^{2T}.B^{2T}}{A^T.B^T} \\\\=\frac{(AB)^{2T}}{(AB)^T} \ \ (factor \ out \ the power)\\\\= (AB)^{2T-T} \ (apply \ division \ law \ of \ indices; \ \frac{x^a}{x^b} = x^{a-b})\\\\= (AB)^T \ (Proved)$