Quiz
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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.
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.
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Given Function & & Inverse Function
y=log_5 (x+1) & swap ⟶ & x=log_5 (y+1)
Now we have to isolate y in the inverse equation. To do this, we can use the definition of a logarithm to rewrite the equation.
Now we have the inverse of the given function. y= 5^x -1
We will begin by graphing y= 5^x -1. To do it, we will make a table of values to find points on its graph.
| x | 5^x-1 | y=5^x-1 |
|---|---|---|
| - 1 | 5^(- 1)-1 | - 0.8 |
| 0 | 5^0-1 | 0 |
| 1 | 5^1-1 | 4 |
| 1.5 | 5^(1.5)-1 | ≈ 10.18 |
Now we will plot and connect the points with a smooth curve.
To draw the graph of y=log_5 (x+1), we need to reflect y=5^x-1 across the line y=x. To do this, we will reverse the coordinates of the points found in the table.
