How do you find all values of x such that f(x) = 0 given f(x) = (1/4)x^3 - 2f(x)=(14)x32?

1 Answer
Jun 1, 2018

Assuming f:RR->RR, then x=2 is the only value which satisfies f(x)=0.

Explanation:

We wish to find the roots of the function

f(x) = (1/4)x^3-2

By root, we mean any value of x for which f(x)=0.

:. (1/4)x^3-2=0 =>(1/4)x^3=2

Multiply both sides by 4.

x^3=8=>color(red)(x=2)

Let this first root we found be x_1. However, we did it algebraically and there seems to be only one solution. Could this be the only one?

Yes. If the function has domain and range over the real numbers RR then x=2 is the only root of f.

We can verify this graphically, too:

graph{(y-1/4x^3+2)=0 [-7.9, 7.9, -3.31, 4.59]}