Use the graph of f to draw the graph of its inverse function. y3-2+1--4-3-2-1112 3 4-3+

Answered: y 3- 2+ 1- -4-3-2-11 12 3 4 -3+

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.4: Subtracting Real Numbers

Problem 48WE

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Question

Use the graph of f to draw the graph of its inverse function.

Expert Solution

Step 1:To determine

Given:

Graph of $f (x)$

To determine:

Graph of inverse function.

Step 2:Calculation

From the given graph of $f (x)$ , the line passes through the points $(2, 0) & (0, - 4)$ .

So, the equation of line is given by:

$y - 0 = \frac{- 4 - 0}{0 - 2} (x - 2) \Rightarrow y = \frac{- 4}{- 2} (x - 2) \Rightarrow y = 2 (x - 2) \Rightarrow y = 2 x - 4$

So, $f (x) = 2 x - 4$

Now, we will determine inverse of a function.

$Let y = 2 x - 4 \Rightarrow y + 4 = 2 x \Rightarrow x = (\frac{y + 4}{2}) So, f^{- 1} (y) = \frac{y + 4}{2} \Rightarrow f^{- 1} (x) = \frac{x + 4}{2} = g (x)$

Now, we will sketch graph of $g (x) = \frac{x + 4}{2}$

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