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If function `f` satisfies the relation `f(x)xf^(prime)(-x)=f(-x)xf^(prime)(x)fora l lx ,a n df(0)=3,a n diff(3)=3,` then the value of `f(-3)` is ______________

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`f(x)cdotf'(-x)=f(-x)cdotf'(x)`
`"or "f'(x)xxf(-x)-f(x)xxf'(-x)=0`
`"or "(d)/(dx)[f(x)f(-x)]=0`
`"or "f(x)f(-x)=k`
`"Given "(f(0))^(2)=k=9 or k=9`
`"Then "f(3)f(-3)=9 or f(-3)=3`
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CENGAGE-DIFFERENTIATION-Exercise (Numerical)
  1. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

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  2. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

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  3. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

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  4. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  5. Prove that (2^((log)2 1/4x)-3^(log)(27)(x^2+1)^3-2x >)/(7^(4(log)(49)...

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  6. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

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  7. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

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  8. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

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  9. f(x) is polynomial of degree 4 with real coefficients such that f(x)=0...

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  10. A nonzero polynomial with real coefficient has the property that f(x)=...

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  11. A function is reprersented parametrically by the equations x=(1+t)/(t^...

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  12. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

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  13. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  14. Let f(x)=x+1/(2x+1/(2x+1/(2x+oo))) Compute the value of f(50)dotf^(p...

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  15. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

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  16. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

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  17. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

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  18. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  19. If x^3+3x^2-9x=c is of the form (x-alpha)^2(x-beta) , then c is equal ...

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  20. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

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