3 years ago

If f(x) = x-6 and g(x) = x^1/2 , find g(x) x f(x) .

Mathematics

1 answer:

shusha [124]3 years ago

5 0

Answer:

x^3/2 - 6x^1/2

Step-by-step explanation:

f(x) = x - 6

g(x) = x^1/2

g(x) * f(x) = x^1/2(x - 6)

g(x) * f(x) = x^3/2 - 6x^1/2

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$\text{L.H.S}\\\\=\dfrac{\sin^4 A - \cos^4 A}{ \sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A)^2-(\cos^2 A)^2}{\sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A + \cos^2 A)(\sin^2 A-\cos^2 A)}{\sin A + \cos A}\\\\\\=\dfrac{1\cdot(\sin A+\cos A)(\sin A - \cos A)}{\sin A +\cos A}\\\\\\=\sin A - \cos A\\\\\\=\text{R.H.S}~~~ \\\\\text{Proved.}$

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