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Let f(x)=2/x-3. Find f^-1(x)

KonstantinChe [14]

Answer:

Two questions:

Question 1: $f^{-1}(x)=?$ given $f(x)=\frac{2}{x}-3$ .

Answer 1: $f^{-1}(x)=\frac{2}{x+3}$

Question 2: $f^{-1}(x)=?$ given $f(x)=\frac{2}{x-3}$ .

Answer 2: $f^{-1}(x)=\frac{2}{x}+3$

Step-by-step explanation:

So $f^{-1}$ is used in most classes to represent the inverse function of $f$ .

The inverse when graphed is a reflection through the y=x line. The ordered pairs $(a,b)$ on $f$ implies $(b,a)$ are on $f^{-1}$ .

This means we really just need to swap x and y.

Since we want to write as a function of x we will need to solve for y again.

Question 1:

$y=\frac{2}{x}-3$

Swap x and y:

$x=\frac{2}{y}-3$

We want to solve for y.

Add 3 on both sides:

$x+3=\frac{2}{y}$

Make the left hand side a fraction so we can cross-multiply:

$\frac{x+3}{1}=\frac{2}{y}$

Cross multiply:

$y(x+3)=1(2)$

Simplify right hand side:

$y(x+3)=2$

Divide both sides by (x+3):

$y=\frac{2}{x+3}$

So $f^{-1}(x)=\frac{2}{x+3}$ .

Question 2:

$y=\frac{2}{x-3}$

Swap x and y:

$x=\frac{2}{y-3}$

Make left hand side a fraction so we can cross multiply:

$\frac{x}{1}=\frac{2}{y-3}$

Cross multiply:

$(y-3)x=1(2)$

We have to distribute here:

$yx-3x=2$

Add 3x on both sides:

$yx=2+3x$

Divide boht sides by x:

$y=\frac{2+3x}{x}$

You could probably stop here but you could also simplify a little.

Separate the fraction into two terms since you have 2 terms on top bottom being dividing by x:

$y=\frac{2}{x}+\frac{3x}{x}$

Simplify second fraction x/x=1:

$y=\frac{2}{x}+3$

So $f^{-1}(x)=\frac{2}{x}+3$ .

7 0

2 years ago

5/26

elena-s [515]

$k =1.89$ is the constant of proportionality that represents the relationship between the cost, y, to the number of pounds of potatoes, x .

<u>Step-by-step explanation:</u>

Here we have , The cost of 2 pounds of potatoes is $3.78. We need to find the constant of proportionality that represents the relationship between the cost, y, to the number of pounds of potatoes, x . Let's find out:

Cost is y & number of pounds of potatoes is x :

$y = (k)x$ , where k is constant of proportionality that represents the relationship between the cost, y, to the number of pounds of potatoes, x .

⇒ $y = (k)x$

⇒ $3.78 = (k)2$

⇒ $\frac{3.78}{2} = \frac{(k)2}{2}$

⇒ $\frac{3.78}{2} =k$

⇒ $k =1.89$

Therefore, $k =1.89$ is the constant of proportionality that represents the relationship between the cost, y, to the number of pounds of potatoes, x .

4 0

3 years ago

Pls help me

daser333 [38]

Answer:

A:(4,2) B:(1,2) C:(1,3)

Step-by-step explanation:

During a rotation 90 degrees ccw the points go from (x,y) to (-y,x)

3 0

3 years ago

Can someone help me with this problem

aleksandr82 [10.1K]