Question

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

Answer 1

Answer:

$x=0$ and $x=1$.

Step-by-step 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:

$x^{2}=\sqrt{x} \\(x^{2} )^{2}=(\sqrt{x} )^{2}\\x^{4}=x\\x^{4}-x=0\\x(x^{3}-1)=0$

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 $x=1$.

Answer 2

Answer:1.5

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