Chapter ISG, Problem 4.7.4P

To determine

To write an inverse of function

Answer to Problem 4.7.4P

  $y=3x+10$

Explanation of Solution

Given information:

  $f(x)=\frac{x-10}{3}$

Calculation:

If function is mapping x to y, then inverse of the function must map y to x .

Let function be: $y=\frac{x-10}{3}$

To find the inverse, change variable,

  $x=\frac{y-10}{3}$

Solvefor y.

  $3x=y-10$

So,

  $y=3x+10$

To determine

To write an inverse of function

Answer to Problem 4.7.4P

  $y=\frac{4x-24}{3}$

Explanation of Solution

Given information:

  $g(x)=\frac{3}{4}x+6$

Calculation:

If function is mapping x to y, then inverse of the function must map y to x .

Let function be: $y=\frac{3}{4}x+6$

To find the inverse, change variable,

  $x=\frac{3}{4}y+6$

Solvefor y,.

  $x=\frac{3y+24}{4}$

Multiplying both sides by 4,

  $4x=3y+24$

Adding 24 to both sides,

  $4x-24=3y$

So,

  $y=\frac{4x-24}{3}$

Inverse of function is $y=\frac{4x-24}{3}$

To determine

To write an inverse of function

Answer to Problem 4.7.4P

  $y=\frac{-(x+7)}{5}$

Explanation of Solution

Given information:

  $h(x)=-5x-7$

Calculation:

If function is mapping x to y, then inverse of the function must map y to x .

Let function be: $y=-5x-7$

To find the inverse, change variable,

  $x=-5y-7$

Solvefor y.

  $x+7=-5y$

Dividing both sides by -5,

  $y=\frac{(x+7)}{-5}$

And,

  $y=\frac{-(x+7)}{5}$

Hence, inverse of the function is $y=\frac{-(x+7)}{5}$ .