Equations, Inequalities and VICs, Chapter 5, p. 81

[nvingers]

At the bottom of the page, there is a question about finding a value of x for which f(g(x)) = g(f(x)).

The book states:

If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does f(g(x)) = g(f(X))?

Simply evaluate as we did in the problem above, using x instead of an input value:

f(g(x)) = g(f(X))

f(2x) = g(x^3 + 1)

AND HERE IS MY QUESTION: HOW DO WE GET FROM THIS LINE TO THE NEXT LINE??

(2x)^3 + 1 = 2(x^3 + 1)

Thanks in advance for helping me out!!

[guest]

you just need to solve the equation for x.

8x^3+1 = 2x^3 +2

6x^3 = 1

x^3 = 1/6

x = 1/sqrt(6)

x = sqrt(6)/6

[Guest]

ah, okay, thanks! i made it out to be more comlicated than it actually is. ;)

[JonathanSchneider]

Note that the big diagonal arrow on this page means that we go from the line that you cited to the top of the next row. In other words, when we present two columns of math in this way, read DOWN the first and then DOWN the second, not side to side throughout. Make sense?