Question

If h(x) = x^2, then h(3x) = 9h(x). Explain algebraically why this happens.

Answer 1

h(x) = x^2

To find h(3x) we let x in the function h(x) be replaced by 3x. Wegetr:

h(3x) = (3x)^2

Now we simplify the right side.

h(3x) = (3x)^2 = 3^6x*2 = 9x^2

Since h(x) = x^2, then 9x^2 is the same as 9h(x).

h(3x) = (3x)^2 = 3^6x*2 = 9x^2 = 9h(x)