Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# How to find inverse function of y= -(3) 2/x-4 -40 ?!?

I have kept trying and trying but I can’t seem to find the proper inverse function, at least not one that looks right. I circled the one I just can’t seem to get. If you are having trouble reading it it’s y= -(3) 2/x-4 -40

Any help is greatly appreciated. Relevance

You have:

y = -3 * 2 / (x - 4) - 40

Before we try to find the inverse function, let's simplify this. We can multiply the first two integers together:

y = -6 / (x - 4) - 40

Now I'll swap the variables and start solving for y again:

x = -6 / (y - 4) - 40

x + 40 = -6 / (y - 4)

Before moving on, I'll simplify this by multiplying both halves of the fraction by -1. This turns the -6 to a 6 and turns the (y - 4) into (4 - y):

x + 40 = 6 / (4 - y)

Now multiply both sides by the denominator:

(x + 40)(4 - y) = 6

Expand the left side:

4x - xy + 160 - 40y = 6

Move all terms that don't have "y" in it to the right side:

-xy - 40y = -4x - 154

Factor out a -y from the right side:

-y(x + 40) = -4x - 154

Then divide both sides by -(x + 40):

y = (4x + 154) / (x + 40)

That's what I get. As a test, let's give x a value into the original equation then solve for y, then substitute that into x into this equation and we should get the starting value back if we did this right. Let's set x = 10:

y = -3 * 2 / (x - 4) - 40

y = -3 * 2 / (10 - 4) - 40

y = -6 / 6 - 40

y = -1 - 40

y = -41

Now put that into the equation we derived:

y = (4x + 154) / (x + 40)

y = (4(-41) + 154) / (-41 + 40)

y = (-164 + 154) / (-1)

y = -10 / (-1)

y = 10

And we do get the starting value so this is the correct inverse function.

Again that function is:

y = (4x + 154) / (x + 40)

• y = -(3)2 / (x - 4) - 40

(y + 40) (x - 4) - 3 x 2Yx - 4y + 40x - 160 = -6x(y + 40) = -6 + 4y + 160x = 4y + 15y / y + 40f⁻¹(y) = 4x + 15y / x + 40.

• so you have y = - 3 { 2 / [ x - 4 ] } - 40 ----> [ y + 40] = - 6 / [ x - 4 ] ---->

x - 4 = - 6 / [ y + 40 ] ---> x = 4 - [ 6 / ( y + 40 ) ] as the decription of the

inverse.......take a number , add 40 to it , divide 6 by that result....

subtract this last result from 4