Asked by Rachel
Find the inverse function g−1(x),
its domain
and its range for
g(x)=40x^2−24, x≥0
can u explain it in baby talk..lol..I have many like this to do...thank you very much
its domain
and its range for
g(x)=40x^2−24, x≥0
can u explain it in baby talk..lol..I have many like this to do...thank you very much
Answers
Answered by
oobleck
g<sup><sup>-1</sup></sup>(x) = ±√((x+24)/40)
So g(x) has no one inverse, since a horizontal line intersects it in more than one place.
Since the domain of g is all reals, and its range is [-24,∞)
both branches of g<sup><sup>-1</sup></sup> have domain [-24,∞)
while one branch has range (-∞,0]
and the other has range [0,∞)
the inverse is a parabola with axis of symmetry y = 0
one branch goes up and the other branch goes down
So g(x) has no one inverse, since a horizontal line intersects it in more than one place.
Since the domain of g is all reals, and its range is [-24,∞)
both branches of g<sup><sup>-1</sup></sup> have domain [-24,∞)
while one branch has range (-∞,0]
and the other has range [0,∞)
the inverse is a parabola with axis of symmetry y = 0
one branch goes up and the other branch goes down
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