Question

Which equation is the inverse of 5y+4 = (x+3)^2 + 1/2?

Answer 1

`f^(-1)(x)=-3(+/-)\sqrt{(10x+7)/(2)}`

Explanation:

we have

`5y+4=(x+3)^(2)+(1)/(2)`

Exchange x for y and y for x

`5x+4=(y+3)^(2)+(1)/(2)`

Isolate the variable y

`5x+4-(1)/(2)=(y+3)^(2)`

`5x+(7)/(2)=(y+3)^(2)`

`(10x+7)/(2)=(y+3)^(2)`

Take square root both sides

`(y+3)=(+/-)\sqrt{(10x+7)/(2)}`

`y=-3(+/-)\sqrt{(10x+7)/(2)}`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=-3(+/-)\sqrt{(10x+7)/(2)}`