1.

Find the range of the function `f(x)=3 sin (sqrt((pi^(2))/(16)-x^(2))).`

Answer» We must have `(pi^(2))/(16)-x^(2) ge0`
Also, `(pi^(2))/(16)-x^(2) le (pi^(2))/(16)`
`implies 0 le(pi^(2))/(16)-x^(2) le (pi^(2))/(16)`
`implies 0 le sqrt((pi^(2))/(16)-x^(2)) le (pi)/(4)`
`implies 0 le sinsqrt((pi^(2))/(16)-x^(2)) le (1)/(sqrt(2))`
`implies 0 le 3sinsqrt((pi^(2))/(16)-x^(2)) le (3)/(sqrt(2))`
Hence, range is `[0,(3)/(sqrt(2))]`


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