Question

f(x) = 3x^2 + 9 and g(x) = (1/3)x^2 - 9 Write simplified expressions for f(g(x)) and g(f(x)) in terms of x

Answer 1

Answer:

f(g(x)) = $\frac{x^{4} }{3} - 12x^{2} + 8$

g(f(x)) = $3x^{4} + 30x^{2} +72$

Step-by-step explanation:

This is a fairly simple idea but long math. How you do this is for the first one you take the function of g(x) and place it instead of the x function of the f(x).

It should look something like this.

f(g(x)) = $(3)(\frac{x^{2} }{3} - 9)^{2} + 9$

Simplifying this equation would yield the answer given above.

I did them by hand, but if you would like get an instant and 100 percent correct answer you can use wolfram alpha.

Hope this helps.