What is the inverse of f ( x ) ? f ( x ) =

Question

1 year ago

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la1" title="\frac{2}{x - 6}" alt="\frac{2}{x - 6}" align="absmiddle" class="latex-formula">

1 answer:

vladimir1956 [14] · Answer 1 · 2024-05-18T00:37:11+03:00

The inverse of f(x) is (6x + 2)/x.

<h3>What is an inverse function?</h3>

The inverse function is defined as a function obtained by reversing the given function.

Given that f(x) = 2/(x-6)

To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.

So after switching x and y,

f(x) = y = 2/(x-6)

becomes

x = 2/(y - 6)

Now, we solve for y regularly.

f(x) = y = 2/(x-6)

Solve for y :

⇒ x(y - 6) =2

⇒ xy - 6x = 2

⇒ y = (6x + 2)/x

Therefore the inverse of f(x) is (6x + 2)/x

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