Question

Find f(g) and g(f) where f(x) = x² + 1 and g(x) = x² are functions from R to R.

Answer 1

To find f(g), substitute g(x) into f(x) and simplify. To find g(f), substitute f(x) into g(x) and simplify.

Step-by-step explanation:

To find f(g), we substitute the function g(x) into f(x) and simplify.

f(g) = f(x²) = (x²)² + 1 = x^4 + 1

To find g(f), we substitute the function f(x) into g(x) and simplify.

g(f) = g(x² + 1) = (x² + 1)² = (x^2 + 1)(x^2 + 1) = x^4 + 2x^2 + 1