Respuesta :

calculista

Answer:

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4-x^{2}[/tex]

Let

y=f(x)

[tex]y=4-x^{2}[/tex]

Exchange the variables x for y and y for x

[tex]x=4-y^{2}[/tex]

Isolate the variable y

[tex]y^{2}=4-x[/tex]

square root both sides

[tex]y=(+/-)\sqrt{4-x}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

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

zainebamir540

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.

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