Question

Determine if the two functions are inverses of one another.
f(x)=√(x+8)+1 g(x)=(x-1)³+8

Answer 1

To determine if f(x) = √(x+8)+1 and g(x) = (x-1)³+8 are inverses, we can check if applying one function undoes the effect of applying the other function.

Step-by-step explanation:

Two functions are inverses of each other if applying one function undoes the effect of applying the other function. To determine if f(x) = √(x+8)+1 and g(x) = (x-1)³+8 are inverses, we can check if applying one function undoes the effect of applying the other function.

To do this, we can:

1. Start with f(g(x)) and simplify it to see if we get x
2. Start with g(f(x)) and simplify it to see if we get x

If both of these results in x, then the two functions are inverses.

Step 1: f(g(x)) = f((x-1)³+8)

Replace g(x) with (x-1)³+ 8 in f(x) = √(x+8)+1

=> f(g(x)) = f((x-1)³+8) = √(((x-1)³+8) + 8) + 1

Simplify this expression and check if it simplifies to x. Repeat this process for g(f(x)) = g(√(x+8)+1).