Does the function 1/(√x-4) have an inverse? if so, how do you know?

Question

It's just a math question

Answer 1

y = 1/(√x-4)

let us first find the inverse

interchange y by x and x by y

x= 1/(√y-4)

solve for y

x^2 = 1 / (y-4)

y-4 = 1/ x^2

y = 1/ x^2  +4

so,

f^-1(x) = 1/x^2 + 4

get the graph of this function.

you will find that it fails the horizontal line test.

so this inverse is not a function.

or

the function 1/(√x-4) has no inverse

Answer 2

y = 1/[sqrt(x) - 4]

Inverse means x = 1/[sqrt(y) - 4] then solve for y.

1/x = sqrt(y) - 4

1/x + 4 = sqrt(y)

(1/x + 4)^2 = y

Answer 3

A function has an inverse if the function is one-to-one (i.e. if f(a) = f(b) then a = b).

I'm assuming you mean:

f(x) = 1/√(x - 4)

This function is one to one.  Therefore, it will have an inverse.

Hope this helps!

Answer 4

yes.  it is (sqrt(x) - 4).  remember that x can not equal 16 because that would be 1/0 which is an irrational number.  x also can not be less than zero as that would be an imaginary number.  inverses are easy.  just multiply by 1 / the function.  there is a button for it on a scientific calculator labelled either 1/x or x^-1.