Question

What is the best approximation for the input value when f(x)=g(x)?

Answer 1

Answer:1.5

Step-by-step explanation: Got it correct on edge.

Answer 2

`x=0` and
`x=1`.

Explanation:

If we have to different functions like the ones attached, one is a parabolic function and the other is a radical function. To know where
`f(x)=g(x)`, we just have to equalize them and find the solution for that equation:

`x^(2)=√(x) \\(x^(2) )^(2)=(√(x) )^(2)\\x^(4)=x\\x^(4)-x=0\\x(x^(3)-1)=0\\`

So, applying the zero product property, we have:

`x=0\\x^(3)-1=0\\x^(3)=1\\x=\sqrt[3]{1}=1`

Therefore, these two solutions mean that there are two points where both functions are equal, that is, when
`x=0` and
`x=1`.

So, the input values are
`x=0` and
`x=1`.