Answer:
Option 2 is the answer.
Step-by-step explanation:
To find the equation for [tex]f^{-1}(x)[/tex] 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.
[tex]f^{-1}(x)[/tex] = x² - 6x + 9 ≅ (x - 3)²
So the answer is [tex]f^{-1}(x)[/tex] = (x - 3)²
Answer:
Choice 2 is correct answer.
Step-by-step 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.
