Question

HELP ASAP! 70 POINTS

Show that the function g(x)=x-2/5 is the inverse of f(x) = 5x + 2.
Step 1: The function notation f(x) can be written as a variable in an equation. Is that variable x or y?
____
Write f(x) = 5x + 2 as an equation with the variable you chose above. (2 points)


Step 2: Switch the variables in the equation from Step 1. Then solve for y. Show your work.


Step 3: Find the inverse of .g(x)=x-2/5 What does this tell you about the relationship between f(x) = 5x + 2 and g(x)? Show your work.

Answer 1

Answer:  f(x) and g(x) are inverses of each other

Step-by-step explanation:

To find the inverse of a function, swap the x's and y's and then solve for "y"

f(x) = 5x + 2

 y  = 5x + 2

Swap:

     x = 5y + 2

   -2        - 2

x - 2 = 5y

÷5     ÷5      

$\dfrac{x-2}{5}=y$

****************************************************************

$g(x)=\dfrac{x-2}{5}\\\\y=\dfrac{x-2}{5}\\\\\text{Swap:}\\x=\dfrac{y-2}{5}\\\\\\(5)x=\dfrac{y-2}{5}(5)\\\\\\5x=y-2\\\\5x+2=y$