Question

Let f(x) = x ¹/2 and g(x) = 2x² . Find (fg) (x) then evaluate the
product when x=9.

Answer 1

see explanation

Explanation:

using the rules of exponents/ radicals

•
`a^(m)` ×
`a^(n)` =
`a^((m+n))`

•
`a^{(m)/(n) }` =
`(\sqrt[n]{a} )^m`

then

(fg)(x)

= f(x) × g(x)

=
`x^{(1)/(2) }` × 2x²

= 2 ×
`x^{((1)/(2)+2) }`

= 2
`x^{(5)/(2) }`

when x = 9 , then

= 2 ×
`9^{(5)/(2) }`

= 2 ×
`(√(9))^5`

= 2 ×
`3^(5)`

= 2 × 243

= 486