A cube has a volume of 10 cm^3. A larger cube has a volume of x cm^3. Consider the function f (x) = (x-10) cubed. What do the values f (19) and f (14) represent?

Hence both F (19) and F (14) has value for their indices.

Step-by-step explanation:

Given:

A cube with volume = 10cm^3

And a function=F (x) = (x-10) ^3.

To find;

Relationship between values at x=19 and x=14.

Solution:

Given that volume of cube = 10 c. c.

So (l) ^3=10 c. c

l = (10) ^ (1/3)

l=2.15544 cm

Now

F (x) = (x-10) ^3

here x=19

F (19) = (19-10) ^3

= (9) ^3

=729 cc

Now for x=14

F (14)

= (14-10) ^3

= (4) ^3

=64 cc

Now concluding from above equation we get,

The values are 729 and 64

These two can be written in same value of index as follows:

(729) = (9) ^3

={ (3) ^2}^3}.

= (3) ^6

And

(64) = (4) ^3

={ (2) ^2}^3

= (2) ^6.

Hence both F (19) and F (14) has value for their indices.