Algebra, Solving equations
posted by Amy .
I'm stuck with this equation:
y = (4x1)/(2x+3)
We're working on inverses, which I understand, but my mind is blanking on how to solve this for x.
Thanks in advance,
Amy :)
after you interchanged the x and y variables, and expanded you should have had
x = 8y^2 + 10y  3
arrange to look like a quadratic equation
8y^2 + 10y  3  x = 0
now a=8, b=10 and c=3x
use the formula to solve for y
notice you get 2 different equations.
Are you also learning about functions?
Oh, this is embarassing...I'm studying inverse functions in calculus and I'm getting hung up on algebra I did in high school. :)
This particular problem's directions say to find the inverse of the given function, but I thought I read that if it's not a onetoone function, it doesn't have an inverse. So if there's two equations once I use the quadratic formula, then this equation doesn't have an inverse, right?
Hold on a sec...There's division between those two terms, so I wouldn't end up getting two different answers, right?
I got y = (10 + sqrt(10032(3x)))/16 for one and
y = (10  sqrt(10032(3x)))/16 for the other, thus 2 distinct equations
recall that taking the inverse of a relation results in a reflection in the line y=x
Your original equation was a parabola opening upwards, so its inverse is a parabola with axis parallel to the xaxis.
so for a given value of x (in the new domain) you now have 2 different values of y, making it NOT a function.
Do you recall something called the "vertical line test" ?
But it's division. I'm dividing (4x1) by (2x+3). I guess my main question is how do I simplify the original equation so that I can solve it for x. I know I can't just factor it because there's no common factors. When I graph the equation on my calculator, it passes both the VLT and the HLT, so it's definitely onetoone.
oops, oops, oops, my mistake, lets back up
I read that as a multiplication, sorry
now it's actually easier:
step 1 of finding inverse: interchange the x and y variables...
y = (4x1)/(2x+3) turns into x = (4y1)(/2y+3)
cross multiply
2xy+3x=4y1
2xy4y=13x or
4y2xy = 1+3x
y(42x) = 1+3x
y = (1+3x)/(42x)
now clearly the original was a function and so is the new one.
test (1,5) in original and (5,1) in new one
Thanks. I was getting so confused!
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