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If f(x)f(y) + 2 = f(x) + f(y) + f(xy) an...

If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then find f(x).

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. f is a function such that f(x + y) = f(x) .f(y),forall x, y in R , if ...

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  2. A real valued function satisfies the relation f(x+y)=f(x)+f(y)+(e^x-1)...

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  3. If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then fi...

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  4. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Determine the for...

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  5. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the conti...

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  6. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

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  7. Let a and b be real numbers such the the function f(x)={(-3ax^2-2,x<1...

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  8. Let m and n be two positive integers greater than 1. if lim(alphararr0...

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  9. The correct statement(s) is (are)

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  10. Let f(x) be a polynomial of degree four having extreme values at x=1 a...

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  11. lim(xrarr0)((1-cos2x)(3+cosx))/(xtan4x) is equal to:

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  12. If the function . g(x)={(ksqrt(x+1),0lexle3),(mx+2,3ltxle5):}is differ...

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  13. Let f:RrarrR be defined as . f(x)={(0, "x is irrational"),(sin|x|,"x i...

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  14. If lim(xrarr0)(axe^x-blog(1+x))/x^2=3 ,then the values of a ,b are res...

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  15. Let [x]denote the greatest integer less than or equal to x . Then the ...

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  16. Let f:RrarrR be differentiable at x=0 . If f(0)=0 and f'(0)=2,then the...

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  17. Let f:RrarrR be such that f(2x-1)=f(x) for all x in R . If f is contin...

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  18. Let fbe any continuously differentiable function on [a,b] and twice di...

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  19. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

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  20. Letf:RrarrR and g:RrarrR be respectively given by f(x)=|x|+1 and g(x)=...

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