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1 vote
3.
Which is the inverse of the function f(x) = x2 - 4?

User Amit Yadav
by
8.7k points

2 Answers

6 votes

Answer:


\boxed{\±√(x+4)}

Explanation:

The inverse of a function is the reverse of the function.


f(x)=x^2 -4


y=x^2-4

Switch variables.


x=y^2-4

Make y as subject.

Add 4 to both sides.


x+4=y^2

Take the square root on both sides.


\±√(x+4) =y

User ABGR
by
8.3k points
3 votes

Answer:


f^(-1) = ±
√(x+4)

Explanation:


f(x) = x^2-4

Replace f(x) by y


y = x^2-4

Exchange x and y


x = y^2-4

Solve for y


x = y^2-4\\

Adding 4 to both sides


y ^2 = x+4

Taking sqrt on both sides

y = ±
√(x+4)

Replacing y by
f^(-1)


f^(-1) = ±
√(x+4)

User Chris Arriola
by
8.1k points

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