find the inverse function f(x)=x/x-4?

Question

1) also find the domain of ( f ) to the negitve 1st power multiplied by x.

2) find the range of ..............f(-1 power)(x)

3) Graph both f(x)=x/x-4 and the inverse

Answer 1

To get the inverse, write y in place of f(x) then switch x and y to get

x = y / (y-4)

Solve this for y by cross multiplying:

x(y-4) = y
xy - 4x = y

xy - y = 4x

y(x-1) = 4x

y = 4x/(x - 1) is f^-1(x)

Question 1 probably means f to the negative one power OF x not MULTIPLIED BY x, as f^-1 is the symbol for the inverse of f. Its domain is all numbers that do NOT cause the bottom of the fraction to equal zero, so all numbers except 1.

2 The range of f inverse = the domain of the original f (since x and y were switched) so see what makes the original have zero on the bottom. x-4 = 0 if x = 4 so the range of f inverse is all numbers except 4.

3 To graph them just pick numbers for x and plug them in to get y. Note that the same numbers reversed will work for f inverse. Example: (8,2) is on f and (2,8) is on f^-1.

Answer 2

y=x(x-4)
yx-4y=x
yx-x=4y
x=4y/(y-1) <-- inverse

x not equal 4

f(x) has asymptotes at y=1 an x=4
f^-1(x) has asymptotes at y=4 and x=1.
They both resemble hyperbolas.