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Let f : [-(pi)/(2), (pi)/(2)] rarr [3, 1...

Let `f : [-(pi)/(2), (pi)/(2)] rarr [3, 11]` defined as `f(x) = sin^(2)x + 4 sin x + 6`. Show that f is bijective function.

Text Solution

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For `-(pi)/(2)` to `(pi)/(2)`, sin x is increasing also `(sin x + 2)^(2)` is increasing, hence f is one-one.
Also, Range `-= [3, 11]` = co-domain `rArr` f is bijective.
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