What is the inverse function of f(x) = 19/x^3

Step-by-step explanation:

1)  Replace f(x) with y:   y = 19/x^3

2) Interchange x and y:  x = 19/y^3

3) Solve this result for y:  xy^3 = 19, or y^3 = 19/x, or

    y = ∛[19/x]

                                                         -1

4.  Replace this y with the label    f    (x) =  ∛[19/x]

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°