Question

Select the correct answer
What is the inverse of the function f(x)=x+1/x

Answer 1

Answer:

$\boxed{\mathrm{B}}$

Step-by-step explanation:

$f(x)=\frac{x+1}{x}$

$y=\frac{x+1}{x}$

Make x as subject.

Multiply both sides by x.

$yx=x+1$

Subtract both sides by x.

$yx-x=1$

Factor out x.

$x(y-1)=1$

Divide both sides by y-1.

$x=\frac{1}{y-1}$

Switch variables.

$y=\frac{1}{x-1}$

Answer 2

Answer:

${f}^{ - 1} (x) = \frac{1}{x - 1}$

Option B is the correct option.

Step-by-step explanation:

Let y = f ( x )

$y = \frac{x + 1}{x}$

Apply cross product property

$xy = x + 1$

Move 'x' to L.H.S and change it's sign

$xy - x = 1$

Take x as common

$x(y - 1) = 1$

$x = \frac{1}{y - 1}$

Replace x by f ⁻¹(x) and y by x

${f}^{ - 1} (x) = \frac{1}{x - 1}$

Hence, Option B is the correct option.

Hope this helps..

Best regards!!