Question

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

Answer 1

Answer:

$f^{-1}(x)=(+/-)\sqrt{4-x}$

Step-by-step 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

$y=(+/-)\sqrt{4-x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=(+/-)\sqrt{4-x}$ -----> inverse function

Answer 2

Answer:

f⁻¹(x) = ±√x-4

Step-by-step 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.