Find the value of p q for which fx 1-sin 3 x 3cos 2 x - if x- 2

f(x)= #160; 1 sin^3x3cos^2x if x lt;π2 p if x=π2 I(1 sin x)(π 2x)^2 if x gt;π2 f(x2)=f(π^ 2 ...

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Bijective Function

Find the valu...

Question

Find the value of $p$ & $q$ for which $f (x) ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, i f x < \frac{π}{2} p, i f x = \frac{π}{2} i s c o n t i n o u s a t x = \frac{π}{2} \frac{q (1 - sin x)}{{(π - 2 x)}^{2}}, i f x > \frac{π}{2} \end{matrix}$

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p

q

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - sin^{3} x}{{cos}^{2} x}, i f x < π / 2 p, i f x = π / 2 \frac{q (1 - sin x)}{(π - 2 x)^{2}}, i f x > π / 2 \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

x = π / 2

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, i f x < \frac{π}{2} a, i f x = \frac{π}{2} \frac{b (1 - sin x)}{{(π - 2 x)}^{2}}, i f x > \frac{π}{2} \end{matrix}

f (x)

x = \frac{π}{2}

a

b

p

q

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, & i f x < \frac{π}{2} p & i f x = \frac{π}{2} \frac{q (1 - sin x)}{(π - 2 x)^{2}} & i f x > \frac{π}{2} \end{matrix}

\frac{π}{2}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, if x < \frac{π}{2} a, if x = \frac{π}{2} \frac{b (1 - sin x)}{(π - 2 x)^{2}}, if x > \frac{π}{2} \end{matrix}

f (x)

x = \frac{π}{2}

f (x) ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - \sqrt{2} sin x}{π - 4 x}, i f x \neq \frac{π}{4} b, i f x = \frac{π}{4} \end{matrix}

x = \frac{π}{4}

b

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