Question

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

Answer 1

Answer:

$\boxed{\±\sqrt{x+4}}$

Step-by-step 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.

$\±\sqrt{x+4} =y$

Answer 2

Answer:

$f^{-1}$ = ± $\sqrt{x+4}$

Step-by-step 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 = ±$\sqrt{x+4}$

Replacing y by $f^{-1}$

$f^{-1}$ = ± $\sqrt{x+4}$