Respuesta :

sid071

Hey there!!

How do we find inverses?

In versing is the just the flip-flop of the x and y.

Given equation :

...f(x) = √(2x-6)

... y = √(2x-6)

... x = √(2y-6)

Square on both sides

... x² = 2y-6

... x² + 6 = 2y

... x² + 6  / 2 = y

Inverse :

f(x) = ( x² + 6 ) / 2

( ii ) f(x) = ( x - 2 )³ + 8

... y = ( x - 2 )³ + 8

... x = ( y - 2 )³ + 8

... x - 8 = ( y - 2 )³

... cube root on both sides

... ∛( x - 8 ) = y - 2

... ∛(x - 8 ) + 2 = y

Inverse :

f(x) = ∛( x - 8 ) + 2

Hope my answer helps!!

grujan50

I will answer 8.a. because the rest you already have.

Proof that the function is one-one is the following

If f(x1)=f(x2) must be x1=x2

In our case we have function f(x)= (x-2)∧3 + 8

(x1-2)∧3 + 8 = (x2-2)∧3 +8 we add to the both sides number (-8) and get

(x1-2)∧3 = (x2-2)∧3  then take the third root (∛) of the both sides and get

x1-2 = x2-2 we add to the both sides number (+2) and get

x1 = x2  So the proof is finished.

Good luck!!!