INVERSE FUCTIONS.......10 PTS.....MATH.....read?

Question

SAYS:

Determine the inverse functions for the functions below. Begin by switching variables in the original function, then solving for the 'new' y. For each case sketch the function and its inverse.

Inverse Variation-

1. y = 1/x

Please show work/explain

10 PTS.

:)

Answer 1

y = 1/x....switch the variables

x = 1/y

The easiest way to isolate y AND get it in the numerator where you want it is to rewrite the equation making both fractions...

x/1 = 1/y....then flip both fractions (perfectly legal !)

1/x = y/1

ANSWER : y = 1/x

What's really cool is that y = 1/x is its own inverse !!

To graph, use a graphing calculator or make and x/y chart (a.k.a. T chart). The graph is a hyperbola that extends into two quadrants on a grid.

Good luck to you !!

P.S. are you chris or are you two just in the same class ?

Answer 2

let y=f(x)=1/x  then x=f `(y)  [applying inverse  f`]

y=1/x =>x=1/y   [multiplying by x/y on both sides]

=>f`(y)=1/y         [since x= f`(y)]

=>f `(x)=1/x    [replacing y with x]

that is the inverse function of given function

Answer 3

you switch the variables by placing y where x is and place x where y is.

for y=1/x, you would switch the variables so the function would be:

x =1/y

the solve for y:

xy =1

y=1/x

you get the same function as before this means that the function of 1/x is the inverse of itself.

Answer 4

its answer is x = 1/y