6:38 PM Wed Apr 29 D 1. Simplify: (4x² – 3x + 8) – (3x2 – 5)
1 answer:
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We will conclude that:
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
<h3>Comparing the domains and ranges.</h3>
Let's study the two functions.
The exponential function is given by:
f(x) = A*e^x
You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:
y > 0.
For the logarithmic function we have:
g(x) = A*ln(x).
As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:
So the range of the logarithmic function is the set of all real numbers.
<h3>So what we can conclude?</h3>- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
If you want to learn more about domains and ranges, you can read:
First term [ a ] = 6.3
Common difference [ d ] = 8.8 - 6.3 = 2.5
Using general term formula,
78.8 = 6.3 + (n-1)*2.5
2.5*(n-1) = 72.5 [ Dividing both sides by 2.5 ]
n-1 = 29
n = 30
Hence, 78.8 is the 30th term in the arithmetic series.
Common difference [ d ] = 8.8 - 6.3 = 2.5
Using general term formula,
78.8 = 6.3 + (n-1)*2.5
2.5*(n-1) = 72.5 [ Dividing both sides by 2.5 ]
n-1 = 29
n = 30
Hence, 78.8 is the 30th term in the arithmetic series.