hi: find the inverse function of 5x - y = 2

NEHA

Junior Member
Joined
Oct 27, 2006
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90
find the inverse function of
5x - y = 2

what do i have to do? can you tell me
 
skeeter said:
swap x and y ... solve for y.

so like this

y = 2 - 5x


or i did...

5x - y = 2
subtract 5x both sides
y = -3

5x - (-3) = 2
5x + 3 = 2
subtract 3 both sides
5x = -1
x = -0.2

put the value in both are correct...
 
Re: hi new here

Hello, NEHA!

NEHA said:
Find the inverse function of\(\displaystyle \L \;\;5x\,-\,y\.=\,2\)

As skeeter said, swap x and y and solve for y.

So:\(\displaystyle \L \;5x\,-\,y\,=\,2\;\;\Rightarrow\;\;5y\,-\,x\,=\,2\)

\(\displaystyle \L \;5y\,=\,2\,+\,x\,\to\,y\,=\,\frac{2}{5}\,+\,\frac{x}{5}\)

Thus the inverse is:\(\displaystyle \L \;f^{- 1}(x)\,=\,\frac{2}{5}\,+\,\frac{x}{5}\)
 
Can this method be also right?

5x - y = 2
-y = 2 - 5x
y = -(2 - 5x) = 5x - 2

So:

y = 5x - 2 or x = 2 + y / 5
 
NEHA said:
Can this method be also right?

\(\displaystyle \L \;[1]5x\,-\,y\,=\,2\)Yes
\(\displaystyle \L \;[2]-y\,=\,2\,-\,5x\)Yes
\(\displaystyle \L \;[3]y\,=\,-(2\,-\,5x)\,=\,5x\,-\,2\)No because you are distributing the negative but the 2 has no negative. If you wanted to make the right side negative you would have to multiply both sides of the equation by a negative number.

So on step [2] lets divide both sides by negative 1:\(\displaystyle \L \;[4]y\,=\,5x\,-\,2\)
That is what you got but your steps weren't correct.


\(\displaystyle \L \;y\,=\,5x\,-\,2\) or \(\displaystyle x\,=\,2\,+\,y\,/5\,\)
.....
No. Once we got this equation we switch the x and y... NOT solve for x. When we switch the
x and y we then solve for y.

\(\displaystyle \L
\begin{array}{l}
[4]\underbrace y_{} = 5\underbrace x_{} - 2 \\
[5]\underbrace x_{} = 5\underbrace y_{} - 2 \\
\end{array}\)

Now solve [5] for y.
 
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