Asked by Anonymous
f(x)=sqrt(x-2) what is the inverse of f?
I got inverse f(x)= x^2+2 however, you need to specify the domain of x.
the answer key says when x=>0
can you please explain why? I thought it would be when x=>2 ?
I got inverse f(x)= x^2+2 however, you need to specify the domain of x.
the answer key says when x=>0
can you please explain why? I thought it would be when x=>2 ?
Answers
Answered by
Steve
domain of f is x >= 2
Note that the range of f inverse is also f >= 2, since x^2 >= 0 for all x.
Since f(x) = √(x-2), f >= 0
because √4 = 2, <b>not</b> ±2!
So, since the range of f is f >= 0, the domain of f inverse is also x >= 0.
f inverse is not 1-1, so you have to take only the branch whose inverse is f(x), namely, where x>=0.
Note that the range of f inverse is also f >= 2, since x^2 >= 0 for all x.
Since f(x) = √(x-2), f >= 0
because √4 = 2, <b>not</b> ±2!
So, since the range of f is f >= 0, the domain of f inverse is also x >= 0.
f inverse is not 1-1, so you have to take only the branch whose inverse is f(x), namely, where x>=0.
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