Chapter ISG, Problem 4.8STP

To determine

To write equation of inverse of linear function

Answer to Problem 4.8STP

Inverse is $\frac{x+5}{2}$

Explanation of Solution

Given information:

Points are (2, -1) and (-1, -7)

Graph:

  

Formula used:

  $y=mx+b$

Calculation:

To find inverse of a linear function, find the function first.

Equation of line is $y=mx+b$ .

According to question, Points are (2, -1) and (-1, -7)

Let, $x_1^{}$ =2, $x_2^{}$ =-1, $y_1^{}$ =-1, $y_2^{}$ =-7

Slope of line, $m=\frac{y_2^{}-y_1^{}}{x_2^{}-x_1^{}}$

Substituting values,

  $m=\frac{-7-(-1)}{-1-(2)}$

Solving,

  $m=\frac{-7+1}{-3}$

So,

Slope of line, $m=2$

Putting value of slope in equation of line,

  $y=2x+b$

By looking at graph, find x -intercept and y -intercept.

y -intercept, b = -5

From above, function of line is: $2x-5$

Now, inverse of the function is,

If a function is mapping x to y, then inverse should map y to x ,

Interchange the variable:

  $x=2y-5$

Solve the function for y ,

  $y=\frac{x+5}{2}$

Hence, inverse of the function is, $\frac{x+5}{2}$ .