Question

Find f of g.f(x) = x2 - 1, g(x) = x2 + 3

Answer 1

f of g = x⁴ + 6x² + 8

Step-by-step explanation:

f(x) = x² - 1, g(x) = x² + 3

f o g(x) means we replace the x in f(x) with the g(x) function

f o g(x) = (x² + 3)² - 1

expanding the bracket:

f o g(x) = (x² + 3)(x² + 3) - 1

= x²(x² + 3) + 3(x² + 3) - 1

= x⁴ + 3x² + 3x² + 9 - 1

collect like terms:

f o g(x) = x⁴ + 6x² + 8

Hence, f of g = x⁴ + 6x² + 8