F(X)= -6X-1 and g(x)=4x^2. select the solution for (fg)(x)

Question

composite functions help

Answer 1

the functions are f(x) = - 6x - 1 and g(x) = 4x^2.

To find (fg)(x) = f(x) * g(x)

                   = (- 6x - 1)(4x^2).

To find the solution of (fg)(x),

(- 6x - 1)(4x^2) = 0

Apply zero product property.

- 6x - 1 = 0 and 4x^2 = 0

- 6x = 1 and x^2 = 0

x = - 1 / 6 and x = 0.

Therefore, solution for (fg)(x) is x = - 1 / 6 and x = 0.  

Answer 2

The functions are f (x ) = - 6x - 1  and g (x ) = 4x ²

(f g)(x ) = ( f og )(x ) = f (g (x ))

Substitute the expression for functioning g  (in this case 4x ² ) for g (x ) in the composition.

= f (4x ²)

Substitute the expression for functioning f  (in this case - 6x - 1) for f (x ) in the composition.

 = - 6(4x ²) - 1

= -24x ² -1

(f g )(x ) = - 24x ² - 1.

Answer 3

The functions are f (x ) = - 6x - 1  and g (x ) = 4x ²

(f g)(x ) = ( f og )(x ) = f (g (x ))

Substitute the expression for functioning g  (in this case 4x ² ) for g (x ) in the composition.

= f (4x ²)

Substitute the expression for functioning f  (in this case - 6x - 1) for f (x ) in the composition.

 = - 6(4x ²) - 1

= -24x ² -1

(f g )(x ) = - 24x ² - 1.

To solve (fg )(x ) = 0

- 24x ² - 1 = 0

-24x ² = 1

x ² = 1/-24

x ² = (0.041i ^2)

x  = sqrt(0.041 i ²)

x  = 0.2 i

Solution for (fg )(x ) is x  = 0.2i .