Question

On your GDC, graph each function and its inverse on the same grid.

$y = \frac{1}{x + 4}$

Accepted Answer

The graph of the inverse of a function reflects two things, one is the function and second is the inverse of the function, over the line $y = \frac{1}{x + 4}$ . This line in the graph passes through the origin and has slope value $1$ . It can be represented as;

$y = f^{- 1} (x)$

which is equal to;

$x = f (y)$

This relation is somewhat similar to $y = f (x)$ , which defines the graph of $f$ but the part of $x$ and $y$ are reversed here. So if we have to draw the graph of $f^{- 1}$ , then we have to switch the positions of $x$ and $y$ in axes.

Generally, the method of calculating an inverse is swapping of coordinates $x$ and $y$ . This newly created inverse is a relation but not necessarily a function.

The original function has to be a one-to-one function to assure that its inverse will also be a function. A function is said to be a one-to-one function only if every second element corresponds to the first value (values of $x$ and $y$ are used only once).

Here we have to draw it using GDC. We will put the equation in calculator we will get the graph of the function $y = \frac{1}{x + 4}$ and its inverse function is $f^{- 1} (x) = - 4 + \frac{1}{x}$ .

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 21: Practice 4

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 21: Practice 4

Questions from Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 21: Practice 4 with Hints & Solutions

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