Cubic Functional Equation

[nycmathguy]

Solve for x. . .Again.

If f(x + (1/x)) = x^3 + [1/(x^3)], what is f(4)?

Enjoy your Tuesday.

 

[MathLover1]

If f(x + 1/x) = x^3 + 1/x^3, what is f(4)?

We know that,

x^3 + 1/x^3=(x + 1/x)^3 -3*x*(1/x)(x + 1/x)
=(x + 1/x)^3 -3(x + 1/x)

Then,

f(x + 1/x) = (x + 1/x)^3 -3(x + 1/x)

Now, put x + 1/x=4 and we get:

f(4) = (4)^3 -3(4)

f(4) = 52

 

[nycmathguy]

If f(x + 1/x) = x^3 + 1/x^3, what is f(4)?

We know that,

x^3 + 1/x^3=(x + 1/x)^3 -3*x*(1/x)(x + 1/x)
=(x + 1/x)^3 -3(x + 1/x)

Then,

f(x + 1/x) = (x + 1/x)^3 -3(x + 1/x)

Now, put x + 1/x=4 and we get:

f(4) = (4)^3 -3(4)

f(4) = 52

We continue with precalculus today and this weekend. As you know, we are now in.Srction 5.3 aka Trigonometric Equations.