Question

Find the inverse function in slope-intercept form of f(x) = -1/2x + 10.

a) y = -2x + 20
b) y = -1/2x - 10
c) y = 2x + 20
d) y = 1/2x - 10

Answer 1

After exchanging variables and solving for y, the inverse function of f(x) = -1/2x + 10 in slope-intercept form is y = 2x - 20, which is not provided in the options.

Step-by-step explanation:

The question asks to find the inverse function of f(x) = -1/2x + 10 in slope-intercept form. To find the inverse function, we first replace f(x) with y to work with the equation y = -1/2x + 10. Then, we switch x and y to create the inverse relationship, resulting in x = -1/2y + 10. Next, we solve for y to express it as a function of x:

1. 
   
3. Multiply both sides by 2 to get rid of the fraction: 2x = -y + 20.
4. 
   
6. Rewrite the equation to isolate y: -y = -2x + 20.
7. 
   
9. Finally, multiply both sides by -1 to get y alone: y = 2x - 20.

Thus, the inverse function in slope-intercept form is y = 2x - 20, which is not one of the options provided. It seems there may have been an error in the options given or a typo in the original function.