Question

Find the inverse of the function on the given domain. f(x)=(x−5)^2, [5,∞)

Answer 1

To answer this question, first, we set the following equation:

`y=(x-5)^2,`

and solve it for x.

Taking the square root, we get:

`\sqrt[]{y}=x-5.`

Adding 5 to both sides of the equation, we get:

`\sqrt[]{y}+5=x.`

Now, we exchange x for y:

`y=\sqrt[]{x}+5.`

Therefore:

`f^(-1)(x)=\sqrt[]{x}+5.`

Answer:

`f^(-1)(x)=\sqrt[]{x}+5.`