Question

Find the f[g(x)] if f(x)= x^4 + 1 and g(x)= x^2

Answer 1

x^8 + 1 = f(g(x))

Explanation:

It helps to take an intermediate step so you can see exactly what is happening.

Start with f(x) = x^4 + 1

Now put g(x) in for the x on the left hand side.

f(g(x)) = x^4 + 1

Remember that this is an intermediate step. It is not really correct. Now on the right hand side, where you see an x, put g(x)

f(g(x)) = (g(x) ^4 + 1

Now the question is correctly written. Where you see g(x) on the right side, put the value for g(x) where g(x) is

g(x) = x^2

f(g(x)) = (x^2)^4 + 1

(x^2)^4 = x^8 Multiply the powers (2 and 4) to get 8.

So the answer is

f(g(x)) = x^8 + 1