Identify the inverse g(x) of the given relation f(x).

Mathematics

1 answer:

Leno4ka [110]3 years ago

8 0

Answer:

g(x) = {(3, 8), (1, 4), (-1,0), (-3, 4);

Step-by-step explanation:

Recall and use the fact that, the domain of a relation becomes the range of its inverse and vice-versa.

Base on the possible answers ,the given relation is f(x) = {(8,3), (4, 1), (0, -1), (4,-3)}

To find an inverse relation for f(x), we need to swap the x and y coordinates of f(x).

The inverse of f(x) will have the ordered pairs: (3,8),(1,4),(-1,0),(-3,-4)

Therefore the correct choice is g(x) = {(3, 8), (1, 4), (-1,0), (-3, 4);

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3 years ago

if the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. Find the number. EXPLAIN PL

ELEN [110]

Answer: The number is: "2 " .
__________________________________________
Explanation:
__________________________________________
Write the expression; which is an equation, as follows:
__________________________________________
" 4x <span>− 12 = 2(-x) " ; in which "x" represents "the number for which we shall solve" .
___________________________________________
Note:

If the "number" = "x" ; the "opposite of the number" = " -x " ;
</span>___________________________________________
Rewrite as: " 4x <span>− 12 = -2x " ;
</span>_____________________________________________
→ Add "12" ; & add "2x" ; to EACH SIDE of the equation:

4x − 12 + 12 + 2x = -2x + 12 + 2x ;

to get: 6x = 12 ;
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Now, divide each side of the equation by "6" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
____________________________________________________
6x / 6 = 12 / 6 ;

to get: x = 2 .
____________________________________________________
Answer: The number is: "2 " .
____________________________________________________
Let us check our answer, by plugging in "2" for "x" in our original equation:
_____________________________________________________
→ " 4x − 12 = 2(-x) " ;

Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

→ " 4(2) − 12 = ? 2(-2) ??

→ 8 − 12 = ? -4 ? ;

→ -4 = ? -4 ?? Yes!
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3 years ago

How to solve the equation 9v = 8 + v

zloy xaker [14]

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand.

The distributive property is used mostly for simplifying parentheses in expressions/equations.

For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac

So, now we can simplify our expression.

6(x + 1) = 6x + 6

Now let's solve your equation.

9v = 8 + v
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v = 1 <-- Divide both sides by 8

So, v is equal to 1.

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