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Andrew [12]
3 years ago
13

If f(x)=2x-6, then f^-1(x)=

Mathematics
2 answers:
mel-nik [20]3 years ago
7 0
F(x) = 2x - 6

y = 2x - 6

Switching y and x and solving for y;

x = 2y - 6

2y = x + 6

y = \frac{x+6}{2}

Hence,

f^{-1} = \frac{x+6}{2}
kolbaska11 [484]3 years ago
5 0
Hi!

Okay, so -

We are going to replace f(x) with the variable y.

So, f(x) = 2x - 6 is now equal to y = 2x - 6.

Now, we are going to swap the variables. Where we once had x, we will now have y. And where we once had y, we will now have x.

So y = 2x - 6 is now equal to x = 2y - 6.

Now, we need to isolate y on one side of the equation. We must do this by getting rid of the -6, and the 2 multiplied by the variable y.

We get rid of these values by doing the inverse of their operation. Since 6 is negative, we will add it to itself in order for it to cancel out. But, when we do something on one side of the equation - we must do it on the other.

So, we will add 6 on both sides.

x + 6 = 2y - 6 + 6.

x + 6 = 2y.

Okay, now - we cannot add x to 6, because they are unlike terms. So, what we do next <span>instead is divide both sides by 2. Remember, we're doing the inverse of the operation. The inverse of multiplication is division, so we will divide both sides by 2.

</span>\frac{x + 6}{2} = 2y / 2.

\frac{x + 6}{2} = y.

Now, we change the y into f^{-1}(x), and we have our inverse.

f^{-1}(x) = \frac{x + 6}{2}.

Hopefully, this helps! =)
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<h3>Answer: It's a linear equation.</h3><h3>It's not a proportional relationship.</h3><h3>Juanita spend $63 on groceries if she spent $30 on transportation.</h3>

Step-by-step explanation: Given equation y=2x+3.

Where x is the amount she spends on transportation, and y is the amount she spends on groceries.

<em>We can see that given equation is in slope-intercept form y=mx+b.</em>

So, it's a linear equation and y=2x+3 is the relationship between x and y linear.

<em>Also, a linear linear equation represents a proportion relationship if y-intercept is 0.</em>

But for the given equation y=2x+3, y-intercept is 3.

Therefore, it's not a proportional relationship.

Now, in order to find how much would Juanita spend on groceries if she spent $30 on transportation, we need to plug x= 30 in given equation.

Therefore,

y = 2(30) +3 = 60+3 = 63.

<h3>So, Juanita spend $63 on groceries if she spent $30 on transportation.</h3>
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