Question

F(x)=x squared g(x)=x+2
find f(g(x)) and g(f(x))

Answer 1

f(g(x)) = (x + 2)² = x² + 4x + 4

g(f(x)) = x² + 2

Explanation:

∵ f(x) = x²

∵ g(x) = x + 2

→ f(g(x)) means substitute x of f(x) by g(x)

∵ f(g(x)) = f(x + 2)

∴ f(x + 2) = (x + 2)²

∵ (x + 2)² = (x)(x) + (x)(2) + (2)(x) + (2)(2)

∴ (x + 2)² = x² + 2x + 2x + 4

→ Add the like terms

∴ (x + 2)² = x² + 4x + 4

∴ f(g(x)) = (x + 2)² = x² + 4x + 4

→ g(f(x)) means substitute x of g(x) by f(x)

∵ g(f(x)) = g(x²)

∴ g(x²) = x² + 2

∴ g(f(x)) = x² + 2