help please

Question

4. Show, algebraically, that f(x) = 4x – 9 and g(x) = (x + 9)/4 are inverse functions.

 

5. Find a rule for the inverse of f(x) = x3 + 1. Then graph both f(x) and f-1(x) on the same coordinate plane.

Answer 1

4) Given f(x) =4x – 9  , g(x) = (x + 9)/4

Let f(x) = y

  ⇒

 y = 4x-9

 ⇒4x = y + 9

x = (y+9)/4 

Once we have "x =", we will switch x and y; the "y =" is the inverse

So the inverse of f(x) = (x+9)/4 

So f(x) = 4x – 9 and g(x) = (x + 9)/4 are inverse functions .

 

5) Given f(x) = x³ + 1

  

                                                                  f(x) = x³ + 1 plot 

Let f(x) = y

  ⇒

 Now y =  x³ + 1

x³ = y -1

So   

                                                           plot