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Which of the following statements are incorrect? `I`. If `f(x)` and `g(x)` are one-one then `f(x)+g(x)` is also one-one. `II `. If `f(x)` and `g(x)` are one-one then `f(x)dotg(x)` is also one-one. `III`. If `f(x)` is odd then it is necessarily one-one? `Ia n dI Ion l y` `b. I Ia n dI I Ion l y` `c. I I Ia n dIon l y` d. `I ,I Ia n dI I I`

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CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If f(x) is an invertible function and g(x)=2f(x)+5, then the value of ...

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  2. Which of the following functions is one-one ? (1)f:R->R defined as f...

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  3. Which of the following statements are incorrect? I. If f(x) and g(x) a...

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  4. Let f : R^+ ->{-1, 0, 1} defined by f(x) = sgn(x-x^4 + x^7-x^8-1) wher...

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  5. Let f(x) :R->R,f(x)={(2x+alpha^2,xge2),((alpha x)/2+10,x lt 2)) If f(...

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  6. Let f: R-> R, be defined as f(x) = e^(x^2)+ cos x, then f is (a) one-o...

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  7. Let A be a non- empty set of real numbers and f:A->A be such that f(f(...

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  8. Let f:[-oo,0)->(1,oo) be defined as f(x)=(1+sqrt(-x))-(sqrt(-x)-x) the...

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  9. Let f:R->[1,oo) be defined as f(x)=log10(sqrt(3x^2-4x+k+1)+10) If f(x)...

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  10. Suppose f is a real function satisfying f(x+f(x))=4f(x) and f(1)=4. Th...

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  11. Consider a differentiable function f:R->R for which f'(0)=ln2 and f(x...

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  12. Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integ...

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  13. The graph of a function y=g(x) is shown in the following figure. If...

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  14. Let f={(1,1),(2,3),(0,−1),(−1,−3)} be a function from Z to Z defined b...

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  15. Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x...

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  16. The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd...

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  17. Let P(x) = x^10+ a2x^8 + a3 x^6+ a4 x^4 + a5x^2 be a polynomial with r...

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  18. If F(x)a n dG(x) are even and odd extensions of the function f(x)=x|x|...

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  19. The graph of a function y=g(x) is shown in the following figure. If ...

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  20. Let f(x) be real valued and differentiable function on R such that f(x...

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