How do you find the inverse of f(x) =( -2x)/(-7-x)f(x)=−2x−7−x?

1 Answer
Mariya T.
Oct 23, 2015

f^-1 (x)= (-7x)/(-2-x)f−1(x)=−7x−2−x

Explanation:

First, change the term f(x)f(x) to yy

Then, switch the x and y values. You should get
x=(-2y)/(-7-y)x=−2y−7−y

Next solve for Y
-multiply x on the left side by (-7-y)(−7−y) to get rid of the denominator, you should get
-7x-yx=-2y−7x−yx=−2y

  • add yxyx to both sides in order to get all the Ys on the same side
    -7x=-2y+yx7x=−2y+yx

  • factor out the y value from the right side
    -7x=y(-2+x)7x=y(−2+x)

  • divide both sides by (-2+x)(−2+x)
    (-7x)/(-2-x)=y−7x−2−x=y

Lastly change the term yy to f^-1 (x)f−1(x) [f inverse of x]
f^-1 (x)= (-7x)/(-2-x)f−1(x)=−7x−2−x

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