What is the range of the exponential function shown below f(x)=2•7^x
1 answer:
This is rather a sneaky question. You don't know exactly what numbers you can use and what numbers not.
For example, are you allowed to use x = - 3. The answer is yes
f(-3) = 2*7^(-3) = 2/7^3 = 2/147.
How about 0? If there is going to be a problem, zero is usually the number that causes the problem.
f(0) = 2*7^(0) = 2 * 1 = 2 and in this case 0 is just fine.
How about positive numbers? No they are all good.
So the range is -∞ < y < ∞
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For this case we propose a system of equations:
x: Let the variable representing the age of the first child of the Smiths
y: Let the variable representing the age of the second child of the Smiths
According to the data of the statement we have to:
From the first equation we have to:
We substitute in the second equation:
We find the solutions by factoring:
We look for two numbers that, when multiplied, result in 132 and when added, result in 23. These numbers are 11 and 12.
Thus, we have that the factorized equation is:
Thus, the solutions are:
So, we can take any of the solutions:
With
Then
Therefore, the ages of the children are 11 and 12 respectively.
Answer:
The ages of the children are 11 and 12 respectively.