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2 years ago

Find (f-g)(x) for the following functions. f(x) = x2-2x-24 g(x) = x+4

Mathematics

1 answer:

elena55 [62]2 years ago

3 0

Answer:

Step-by-step explanation:

f(x) = x² - 2x - 24

g(x) = x + 4

To find (f-g)(x) subtract g(x) from f(x)

That's

(f-g)(x) = x² - 2x - 24 - ( x + 4)

(f-g)(x) = x² - 2x - 24 - x - 4

Group like terms

We have

(f-g)(x) = x² - 2x - x - 24 - 4

Simplify

We have the final answer as

Hope this helps you

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ANSWER

EXPLANATION

For a matrix A of order n×n, the cofactor $C_{ij}$ of element $a_{ij}$ is defined to be

$C_{ij} = (-1)^{i+j} M_{ij}$

$M_{ij}$ is the minor of element $a_{ij}$ equal to the determinant of the matrix we get by taking matrix A and deleting row i and column j.

Here, we have

$C_{11} = (-1)^{1+1} M_{11} = M_{11}$

M₁₁ is the determinant of the matrix that is matrix A with row 1 and column 1 removed. The bold entries are the row and the column we delete.

$\begin{aligned} A=\begin{bmatrix} \bf 1 & \bf -6 & \bf -4\\ \bf 7 & 0 & -3 \\ \bf -9 & 8 & -8 \end{bmatrix} \implies M_{11} &= \text{det}\left(\begin{bmatrix} 0&-3 \\ 8&-8 \end{bmatrix} \right) \end{aligned}$

Since the determinant of a 2×2 matrix is

$\det\left( \begin{bmatrix} a & b \\ c& d \end{bmatrix} \right) = ad-bc$

it follows that

so $C_{11} = M_{11} = 24$

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