Use the mapping shown above to show the value of the function f(x) at each point.

Mathematics

1 answer:

julsineya [31]2 years ago

7 0

Answer:

The value of the function f(x) at each point is f(-1) = 5, f(0) = 3, f(1) = 5, f(2) = 11, f(3) = 21 ⇒ A

Step-by-step explanation:

Let us use the mapping shown to solve the question

∵ f(x) = y

∵ x is the domain

∵ y is the range

→ From the figure use x from the domain and y from the range, where

each arrow pointed at the corresponding value y of x

∵ x = -1 and the corresponding value of y is 5

∴ f(-1) = 5

∵ x = 0 and the corresponding value of y is 3

∴ f(0) = 3

∵ x = 1 and the corresponding value of y is 5

∴ f(1) = 5

∵ x = 2 and the corresponding value of y is 11

∴ f(2) = 11

∵ x = 3 and the corresponding value of y is 21

∴ f(3) = 21

The value of the function f(x) at each point is f(-1) = 5, f(0) = 3, f(1) = 5, f(2) = 11, f(3) = 21

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Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

marin [14]

Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation: The given system of linear equations is :

$2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

$D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.$

Now, from equations (ii) and (iii), we have

$x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

$2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.$