Question

Find the inverse of f(x)=4-x^2. HELP!!

Answer 1

f⁻¹(x) = ±√x-4

Explanation:

We have given a function.

f(x) = 4-x²

We have to find the inverse of given function.

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

y = 4-x²

Adding -4 to both sides of equation, we have

y-4 = 4-x²-4

y-4 = -x²

x² = 4-y

Taking square root to both sides of above equation, we have

x = ±√4-y

Putting x = f⁻¹(y) , we have

f⁻¹(y) = ±√4-y

Replacing y by x, we have

f⁻¹(x) = ±√x-4 which is the answer.

Answer 2

`f^(-1)(x)=(+/-)√(4-x)`

Explanation:

we have

`f(x)=4-x^(2)`

Let

y=f(x)

`y=4-x^(2)`

Exchange the variables x for y and y for x

`x=4-y^(2)`

Isolate the variable y

`y^(2)=4-x`

square root both sides

`y=(+/-)√(4-x)`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=(+/-)√(4-x)` -----> inverse function