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3 years ago

If f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x).

Mathematics

1 answer:

Alexxx [7]3 years ago

4 0

Answer:

4x + 1

Step-by-step explanation:

Multiply f + g by x because f + g is in parenthesis:

f(x) + g(x)

Then implement equation #1 for f(x) into our equation:

3x - 1 + g(x)

Then implement the other equation for g(x) into our equation:

3x - 1 + x + 2

Then switch the positions of -1 and +x:

3x + x - 1 + 2

Simmplify:

4x + 1

Pls consider giving my answer the Brainliest! Because it would help and mean a lot! ; )

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The matrix form of given linear system is

$\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

Step-by-step explanation:

Let as assume that

$X=\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

Given differential equations are

$\frac{dx}{dt}=-8x+7y-9z$

$\frac{dy}{dt}=5x-y$

$\frac{dz}{dt}=10x+7y+8z$

We need to find the matrix form of given linear system.

Write the elements of left side in a column matrix.

Write all the coefficients in one matrix first which is called a coefficient matrix. Multiply coefficient matrix with the variables matrix and equate left and right side.

$\begin{bmatrix}\frac{dx}{dt}\\ \frac{dy}{dt}\\ \frac{dz}{dt}\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

It can be written as

$\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

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