Question 1

Let f(x)=3 ×^2 tan((pi)(x)/2), where -1 <×<1 a) find f^-1 (3) b) find f (f^-1 (5))

Question 2

$f(x) = 3x^(2)tan((\pi x)/(2))$

$f(x) = 3x^(2)[(1 - cos(\pi x))/(sin(\pi x))]$

$f(x) = 3x^(2)[csc(\pi x) - cot(\pi x)]$

$f(x) = 3x^(2)csc(\pi x) - 3x^(2)cot(\pi x)$

$y = 3x^(2)csc(\pi x) - 3x^(2)cot(\pi x)$

$x = 3y^(2)csc(\pi x) - 3y^(2)cot(\pi x)$

$x = 3y^(2)csc(\pi x) - 3y^(2)cot(\pi x)$

$3 = 3y^(2)csc(\pi x) - 3y^(2)cot(\pi x)$

$3 = 3y^(2)[csc(\pi x)] - 3y^(2)[cot(\pi x)]$

$3 = 3y^(2)[csc(\pi x) - cot(\pi x)]$

$3 = 3y^(2)[(1 - cos(\pi x))/(sin(\pi x))]$

$3 = 3y^(2)tan((\pi)/(2)y)$

$1 = y^(2)tan((\pi)/(2)y)$

$(1)/(tan((\pi)/(2)y)) = y^(2)$

$cot((\pi)/(2)y) = y^(2)$

$cot^(-1)[cot((\pi)/(2)y)] = cot^(-1)(y^(2))$

$(\pi)/(2)y = cot^(-1)(y^(2))$

$\pi y = 2cot^(-1)(y^(2))$

$y = (2cot^(-1)(y^(2)))/(\pi)$

$x = 3y^(2)csc(\pi x) - 3y^(2)cot(\pi x)$

$5 = 3y^(2)csc(\pi x) - 3y^(2)cot(\pi x)$

$5 = 3y^(2)[csc(\pi x)] - 3y^(2)[cot(\pi x)]$

$5 = 3y^(2)[csc(\pi x) - cot(\pi x)]$

$5 = 3y^(2)[(1 - cos(\pi x))/(sin(\pi x))]$

$5 = 3y^(2)tan((\pi)/(2)y)$

$1(2)/(3) = y^(2)tan((\pi)/(2)y)$

$(5)/(3tan((\pi)/(2)y)) = y^(2)$

$1(2)/(3)cot((\pi)/(2)y) = y^(2)$

$\sqrt{1(2)/(3)cot((\pi)/(2)y)} = y$

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