If f x-x2 and g x- sin2x- the value of g f-y-

f(x)= x ^ 2 , f(√( y ) )= (√( y ) ) ^ 2 =y g(x)=sin (2x) g(f(x))=sin (2f(x)) g(f(√( y ) ))=sin 2y ...

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Solving Linear Differential Equations of First Order

If f x=x2 a...

Question

If $f (x) = x^{2}$ and $g (x) = sin (2 x)$ ; the value of $g (f (\sqrt{y})) =$

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Solution

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f (x) =

x^{2}

g (x) = 2 x

f (g (- 3)) - g (f (- 3))

f (x) = 2 x^{3}

g (x) = 3 x

g (f (- 2)) - f (g (2))

If $g {f (x)} = | s i n x |$ and $f {g (x)} = (s i n \sqrt{x})^{2}$ , then

g (f (x)) = |\sin x| and f (g (x)) = {(\sin \sqrt{x})}^{2}, then

f (x) = \sin^{2} x, g (x) = \sqrt{x}

f (x) = \sin x, g (x) = | x |

f (x) = x^{2}, g (x) = \sin \sqrt{x}

f (x) = x^{3}

g (x) = s i n 2 x

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