Question

What’s the inverse equation? And how you solved it step by step please!

Answer 1

Answer: The inverse is
`n(x) = (-2x+1)/(x)`

This is the fraction (-2x+1) all over x

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Work Shown:

Let n(x) be the inverse of m(x)

Replace m(x) with y, swap x and y, then solve for y to determine n(x)

`m(x) = (1)/(x+2)\\\\y = (1)/(x+2)\\\\x = (1)/(y+2)\\\\x(y+2) = 1\\\\xy+2x = 1\\\\xy = -2x+1\\\\y = (-2x+1)/(x)\\\\n(x) = (-2x+1)/(x)\\\\`

Since n(x) is the inverse of m(x), we have these two properties

• m( n(x) ) = x
• n( m(x) ) = x

I'll leave it to you as an exercise to prove those two statements above.

Effectively, whatever the output of one function is the input of the other function, and overall the result is x. Whatever the initial input is, the final output is that initial input. One function undoes the other, and vice versa.