Question

Drag the expressions to the correct functions. Not all expressions will be used. Consider the functions f and g. f(x)=4x^2+1 g(x)=x^2-3 Perform the function compositions.

Answer 1

Answer:

(f o g)(x) = 4x⁴ - 96x + 37

(g o f)(x) = 16x⁴ + 8x² - 2

Step-by-step explanation:

Since, the given functions are,

f(x) = 4x² + 1

g(x) = x² - 3

(f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

         = 4(x⁴ - 24x + 9) + 1

         = 4x⁴ - 96x + 36 + 1

         = 4x⁴ - 96x + 37

(g o f)(x) = g[f(x)]

             = (4x² + 1)²- 3

             = 16x⁴ + 8x² + 1 - 3

             = 16x⁴ + 8x² - 2

Therefore, out of the given options only two expressions are correct.