Because the original duty isn"t "one-to-one," the only has actually an train station if us restrict that is domain.

You are watching: Inverse of y=2^x

If us restrict the domain of the original role to (-∞, 0), -√<( x - 3 ) / 2 > is the inverse

If us restrict the domain the the original function to (0, ∞ ), √<( x - 3 ) / 2 > is the inverse

Note that the points (0,3) and (3,0) are ambiguous......they might belong to either restricted function and its respective inverse.

Here"s a graph......https://www.desmos.com/calculator/bnxeffgjt3

Both the resticted domain functions and also their particular inverses are symmetric come the heat y = x.......as we would expect.......

CPhill May 16, 2015

#1 +121059
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y=2x^2 + 3 subtract 3 from both sides

y - 3 = 2x^2 divide both political parties by 2

/ 2 = x^2 take it the square source of both sides

±√<( y - 3 ) / 2 > = x "swap" x and also y

±√<( x - 3 ) / 2 > = y for y, write f-1(x) signifying the inverse

f-1(x) = ±√<( x - 3 ) / 2 >

Because the original role isn"t "one-to-one," it only has an inverse if we restrict that is domain.

If we restrict the domain of the original function to (-∞, 0), -√<( x - 3 ) / 2 > is the inverse

If we restrict the domain that the original role to (0, ∞ ), √<( x - 3 ) / 2 > is the inverse

Note that the clues (0,3) and also (3,0) are ambiguous......they can belong come either limited function and also its corresponding inverse.

Here"s a graph......https://www.desmos.com/calculator/bnxeffgjt3

Both the resticted domain functions and their particular inverses room symmetric come the heat y = x.......as we would certainly expect.......

CPhill May 16, 2015

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