What is the inverse of 1/√(x-4)?

Question

the square root is over x-4, not just the x

Answer 1

y = 1/√(x - 4)

Interchange x and y:

x = 1/√(y - 4)

Now solve for y:

√(y - 4)x = 1

Square both sides:

(y - 4)x² = 1

yx² - 4x² = 1

yx² = 1 + 4x²

y = (1 + 4x²)/x²

Hope this helps!

Answer 2

f(x) =  1/√(x-4)

y = 1/√(x-4)

Inverse function typically swap x & y and resolve for new y

x =  1/√(y-4)

√(y-4) = 1/x

y-4 = (1/x)²

y = (1/x)² + 4

f inverse(x) = (1/x)² + 4

Answer 3

The multiple inverse = √(x-4)

The addition inverse = -1/√(x-4)

Answer 4

√(x-4)/1

Answer 5

(1+4x^2)/x^2 but i'm not sure