Math Word Problem

Question

Consider the function f(x)=-1/2x+5
1. Write an equation for the inverse of f(x)
2. Use composition to show that f(x) and the equation you wrote are inverses
3. Sketch a graph of f and its inverses
4. How can you verify the graph of f and its inverse that they are indeed inverse
5. Is the inverse of (x) a function? Explain

 

Please give the answers I want to make sure if my answers are right  

Answer 1

1. y = -1/2x + 5

x = -1/2y + 5

1/2y = -x + 5

y = -2x + 10

f'(x) = -2x + 10

 

2. f(f'(x)) = -1/2(-2x + 10) + 5 = x - 5 + 5 = x

 

The rest is on you.