HELP ASAP! 70 POINTSShow 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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Answer: f(x) and g(x) are inverses of each otherStep-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 + 2Swap: 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]