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If functions are inverse, one is a reflection of the other across the line y=x.
Let's begin by finding the inverse. Then, we will graph the inverse and the given function.
Note that the natural logarithm has the number e as its base. Therefore, ln x= log_e x.
y = ln (x-7) ⇔ y = log_e (x-7)
To find the inverse of a function, we start by exchanging the variables in the given function. Then we can solve for y. Note that the inverse of a logarithmic function is an exponential function.
Now we have the inverse of the given function. y= e^x + 7
We will begin by graphing y= e^x + 7. To do it, we will make a table of values to find points on its graph. Note that e ≈ 2.72.
| x | e^x+7 | y= e^x + 7 |
|---|---|---|
| - 1 | e^(- 1)+7 | ≈ 7.37 |
| 0 | e^0+7 | 8 |
| 1 | e^1+7 | ≈ 9.72 |
| 2 | e^2+7 | ≈ 14.39 |
Now we will plot and connect the points with a smooth curve.
To draw the graph of y=ln (x-7), we need to reflect y=e^x+7 across the line y=x. To do this, we will reverse the coordinates of the points found in the table.
