Let f(x)=e^x+3 show that f^-1(x)=ln x-3 can someone explain this to me
1 answer:
Explanation:
For a function ...
y = f(x)
the inverse function is ...
x = f(y)
To write that in the form y=f^-1(x), you need to solve for y.
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For your function f(x) = e^x +3 this looks like ...
x = e^y +3
x -3 = e^y . . . . . subtract 3
ln(x -3) = y . . . . . take the natural log
So, we can write ...
f^-1(x) = ln(x -3)
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Attached is a graph of these functions. As you might guess from the interchange of x and y, a function and its inverse are mirror images of each other across the line y=x.
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Answer:
10 number of checks.
Cost = $6
Step-by-step explanation:
Given that:
Fixed Charges of first bank = $5
Charges of first bank per check = $0.10
Fixed Charges of second bank = $4
Charges of second bank per check = $0.20
To find:
Number of checks such that the charges for the banks become the same?
Solution:
Let the number of checks =
Cost for the first bank for checks = $5 + $0.10
Cost for the second bank for checks = $4 + $0.20
As per question statement, both the costs are the same.
Comparing the values:
So, for 10 number of checks the cost will be same.
The cost = 4 + 0.20 10 = <em>$6</em>