Question

If `f(x) = x - 6` and `g(x) = x^(1/2)(x + 3)`, find `g(x) xx f(x)`.

A.
`root(5)(x^2) - 3root(3)(x^2) - 18x^(1/2)`

B.
`sqrt(x^5) - 3sqrt(x^3) - 18sqrt(x)`

C.
`sqrt(x^5) - sqrt(x^3) - 6sqrt(x)`

D.
`sqrt(x^5) - 3x^3 - 18sqrt(x)`

Answer 1

Answer : option B

Given

f(x) = x - 6

g(x)= √x (x + 3)

We need to find g(x) * f(x)

( x - 6) * (x + 3) √x

we use FOIL method to multiply (x-6)(x+3)

($x^{2} - 3x -18$ ) * sqrt(x)

Now apply exponential property to multiply each terms with sqrt(x)

$x^{2}$ times sqrt(x) becomes \[sqrt(x^5)\]

-3x times sqrt(x) becomes \[-3sqrt(x^3)\]

-18 times sqrt(x) becomes -18sqrt(x)

So final answer is B

\[sqrt(x^5)\] - \[3sqrt(x^3)\] -18sqrt(x)