Question

For x € R, the functions f and g are defined by
f(x)=2x^3.
g(x) = 4x - 5x^2

Answer 1

`(1)/(2^4)\\\\\textrm{or}\\\\2^(-4)`

Explanation:

`f\left((1)/(2)\right) = 2\left((1)/(2)\right) ^3\\\\= 2* (1^3)/(2^3)\\\\=2* (1)/(8)\\\\= (1)/(4)\\\\f^2\left((1)/(2)\right) =\left[ f((1)/(2))\right] ^2 = \left((1)/(4)\right)^2\\\\= (1)/(16)\\\\16 = 2^4\\\\\rm Hence \\f^2\left((1)/(2)\right)= (1)/(2^4)\\\\\textrm {which can be written as }2^(-4)`

since
`(1)/(a^m) = a^(-m)`

Answer 2

2^(-4).

Explanation:

f^2(x) = (2x^3)^2

f^2(1/2) = (2(1/2)^3))^2

= (2 * 1/8)^2

= (1/4)^2

= 1/16

= 2^(-4)