range of the function f(x) = sin^-1x is equal to
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Step-by-step explanation:f(x)=sin
−1
x+2tan
−1
x+x
2
+4x+1
Domain of f(x) is [−1,1]
f
′
(x)=(
1−x
2
1
)+(
1+x
2
2
)+(2x+4)
f
′
(x)>0 in the given domain.
Hence f(x) is an increasing function in the domain.
∴f(x)
min.
=f(−1)=−
2
π
+2(
4
−π
)+1−4+1=−π−2
∴f(x)
max.
=f(1)=
2
π
+2.
4
π
+1+4+1 =π+6
∴ Range of f(x) is [−π−2,π+6]
⇒p+q=4
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