composite functions 2

explain please

yh ok thanks, but one thing. g(x)= (1+2x)^.5 has a valid inverse namely g^-1(x)=(x^2 - 1)/2

isn;t thant many to one e.g. x=5 and x=-5 give you the same y

yh ok thanks, but one thing. g(x)= (1+2x)^.5 has a valid inverse namely g^-1(x)=(x^2 - 1)/2

isn;t thant many to one e.g. x=5 and x=-5 give you the same y

By convention, (1+2x)^.5 is the positive square root only. That means that its inverse is actually only half of the parabola (x^2 - 1)/2, namely:

$(x^2 - 1)/2$, $x \geq 0$.

Because think about it, the point $(-1,0)$ is in the inverse iff $(0,-1)$ is in the original function. But $g(0)=1$, not -1. (because ^0.5 gives you only the positive square root), so this is not true.

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To answer your original question, a function needs to map each domain value to at most 1 range value. (That's by definition of a function.) So you can't have f(3) = 2 and f(3) = -2, for instance.