Description
| If f(x) = 2x – 7, what is the equation for f^-1(x)? |
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Explanation & Answer
(x) = -2x - 7
y = f(x) = -2x -7
then solve for x:
-2x = y + 7
x = (y+7)/(-2) = (-y-7)/2
rewrite in terms of x:
f^(-1)(x) = (-x-7)/2
Compose the inverse f^(-1) with the function f. then input x.
f^(-1) o f(x) = f^(-1)(-2x-7) = [-(-2x-7) - 7]/2 = [+2x + 7 - 7]/2 = 2x/2 = x
for all values of x
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