Question

If f(x) =
`√(x) +3`, what is the equation for f–1(x)?

f–1(x) = x2 - 3

f–1(x) = (x - 3) 2

f–1(x) = x2 + 3

f–1(x) = (x + 3) 2

Answer 1

Choice 2 is correct answer.

Explanation:

We have given a function. we have to find its inverse.

f(x) = √x+3

Putting f(x) = y in above equation, we have

y = √x+3

Separating √x from above equation, we have

y-3 = √x

Taking square to both sides of above equation, we have

(y-3)² = (√x)²

(y-3)² = x

Swapping above equation, we have

x = (y-3)²

Putting x = f⁻¹(y) in above equation, we have

f⁻¹(y) = (y-3)²

Replace y with x.

f⁻¹(x) = (x-3)² which is the answer.

Answer 2

Option 2 is the answer.

Explanation:

To find the equation for
`f^(-1)(x)` we will fist write the function in the form of equation.

y = √x +3

√x = y - 3

x = (y - 3)² = y² - 6y + 9

Now we will replace y as x to write inverse of function f(x).

We will rewrite the equation in the form of function.

`f^(-1)(x)` = x² - 6x + 9 ≅ (x - 3)²

So the answer is
`f^(-1)(x)` = (x - 3)²