Chapter ISG, Problem 4.7.3P

To determine

To find the relation between two lines.

Answer to Problem 4.7.3P

Multiplicative inverse.

Explanation of Solution

Given information:

Two lines that are inverse of one another.

Calculation:

According to question, Lines are inverse, hence,

Function of line 1^st: $f(x)=mx+c$

Function of line 2^nd: $f^{-1}(x)=m{(x)}^{-1}+c$

The slopes of the graphs are also inverse. It means, if slope of 1^st line is m, so the slope of

second line must be $\frac{1}{m}$ .

Hence, it means, the slope of graphs are multiplicative inverse of each other.

To determine

To find relationship between intercept of two inverse lines.

Answer to Problem 4.7.3P

  $x$ -intercept of $f^{-1}(x)$ becomes $y$ -intercept of $f(x)$ . Same happens with other intercept.

Explanation of Solution

Given information:

x and y intercepts of two inverse lines.

The intercepts of the two lines which are inverse acts opposite to each other.

The domain of function $f(x)$ becomes the range for the function $f{(x)}^{-1}$ .

For example: let us assume function: $f(x)=\{(40,50),(10,20)\}$

Domain of the function is {40, 10}

Range of the function is {50, 20}

The inverse of the same function is $f^{-1}(x)=\{(50,40),(20,10)\}$

Here, domain is {50, 20} and range is {40, 10}.

In simple words, $x$ -intercept of $f^{-1}(x)$ becomes $y$ -intercept of $f(x)$ . Same happens with other intercept.