The following function is one to one.  Find the inverse.  Find the domain and range of f and f^-1 f(x)=8x-8

2 Answers

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to write the function such that: `y = 8x - 8` .

You need to write the function in terms of x to find its inverse such that:

`8x = y + 8 =gt x = (y+8)/8`

Hence, the inverse to function f(x) is `f^(-1)(x) = (x+8)/8` .

Since the equation of the inverse function holds for each real value of x, hence the domain of inverse function is the real set R and the range is also R.

Hence, the real set R stands for domain and the range of the inverse function `f^(-1)(x)=(x+8)/8` .

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jebjeb | eNotes Newbie

Posted on

The key point above was the exchange of x with y.

This inverts the function (and the plotted line).

(some "reliable" sources get inverses wrong, such as treating

temperature conversion "converse forms" as inverse functions)