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.

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tramserran tramserran · Answer 1 · 2019-06-18T11:59:41+02:00

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

[tex]\dfrac{x-2}{5}=y[/tex]

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

[tex]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[/tex]