Question

Select the correct answer. If f(x)=x-6 and g(x)=x^1/2(x+3), find g(x) x f(x).

Answer 1

`g(x)*f(x)=x^(5/2)-3x^(3/2)-18x^(1/2)`

Explanation:

To solve this prooblem you must multiply the function f(x) by g(x).

Therefore, you obtain the following result:

`g(x)*f(x)=(x^(1/2)(x+3))(x-6)\\g(x)*f(x)=(x^(3/2)+3x^(1/2))(x-6)\\g(x)*f(x)=x^(5/2)-6x^(3/2)+3x^(3/2)-18x^(1/2)\\g(x)*f(x)=x^(5/2)-3x^(3/2)-18x^(1/2)`

Finally the correct answer is:

`g(x)*f(x)=x^(5/2)-3x^(3/2)-18x^(1/2)`

Answer 2

g(x)*f(x)= x^5/2 - 3x^3/2 -18x^1/2

Explanation:

Given: f(x) = x - 6 and g(x) = √x (x + 3)

Here we have to multiply g(x) and f(x)

g(x) * f(x) = √x(x + 3) * (x - 6)

= √x (x + 3)(x) - √x(x + 3)6

= x^2 √x + 3√x x - 6x√x - 18√x

Now simplify the like terms, we get [x^1/2 = √x]

g(x)*f(x)= x^5/2 - 3x^3/2 -18x^1/2

Hope this will helpful.

Thank you.