Answer:
Domain : {x | all real numbers} ; Range: {y | y > 0}
Step-by-step explanation:
The function can be written as :
![f(x)=\sqrt[\frac{2}{3}]{108^{2\cdot x}}\\\\\implies f(x)=(108)^{(\frac{3}{2})^{2\cdot x}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B%5Cfrac%7B2%7D%7B3%7D%5D%7B108%5E%7B2%5Ccdot%20x%7D%7D%5C%5C%5C%5C%5Cimplies%20f%28x%29%3D%28108%29%5E%7B%28%5Cfrac%7B3%7D%7B2%7D%29%5E%7B2%5Ccdot%20x%7D%7D)
Now, since x is exponent so it can take any real values. So, its domain of f(x) is all real numbers
But value of f(x) can not be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1
So, Range of f(x) is all real numbers greater than 0
Hence, Domain and Range of f(x) is given by :
Domain : {x | all real numbers} ;
Range: {y | y > 0}
For this item, we may let x be the number or liters of apple juice present in the ginger ale. The total volume of the punch then becomes
total volume = 2 + x
Then, considering that 75% of this is apple juice,
x/(2 + x) = 0.75
x = 0.75(2 + x) = 1.5 + 0.75x
x = 1.5 + 0.75x
Also, for this item, the vaue of x is equal to 6 liters.
There is 3600 seconds per hour.
Multiply the speed per second by 3600 to get the speed in miles per hour then convert to kilometer/hour.
4.9 * 3600 = 17,640 miles per hour
17,640 x 1.6 = 28,224 kilometers per hour