Question

Help please!

Find the inverse equation of this function
f(x) = (x + 6)^2 + 1

Thank you!!

Answer 1

Explanation:

you're just going to switch x and y and then solve for y

Answer 2

Hello,

Explanation:

The problem is that the inverse function is not a function but

an union of 2 functions.

`y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-√(x-1) ) * ((y+6)+√(x-1)) =0\\\\y=-6+√(x-1)-6\ or\ y=-6-√(x-1)\\`

For the fun

,
`f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^(-1)(x)=-6-√(x-1) =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^(-1)(x)=-6+√(x-1) =0\ if\ x\geq 6\\`