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Let f: R->R be a function such that f(x...

Let `f: R->R` be a function such that `f(x)=a x+3sinx+4cosxdot` Then `f(x)` is invertible if (a)`a in (-5,5)` (b) `a in (-oo,5)` (c)`a in (-5,+oo)` (d) none of these

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let A(p^2,-p),B(q^2, q),C(r^2,-r) be the vertices of triangle ABC. A p...

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  2. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

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  3. Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x...

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  4. Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)...

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  5. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then (a)k<3...

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  6. Let f: \mathbb{R} rarr \mathbb{R} be a twice differentiable function s...

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  7. Show that 5xlt=8sinx-sin2xlt=6x for 0lt=xlt=pi/3dot

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  8. Discuss the number of roots of the equation e(k-xlogx)=1 for different...

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  9. Prove that sin1>cos(sin1)dot Also, show that the equation sin("cos"(si...

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  10. Pa n dQ are two points on a circle of centre C and radius alpha . The ...

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  11. If f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)+(lambda^2-5...

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  12. Let f(x)={(2-|x^2+5x+6|,x!=-2),(a^2+1,x=-2):} then value of 'a' so tha...

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  13. If A >0,B >0 and A+B=pi/3, the maximum value of tanAtanB is

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  14. f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasi...

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  15. If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a...

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  16. The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot The...

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  17. Iff(x)={sin^(-1)(sinx),x >0, pi/2,x=0,tcos^(-1)(cosx),x<0

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  18. f: R to R ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot ...

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  19. Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^...

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  20. If f: RtoRa n dg: RtoR are two functions such that f(x)+f^(primeprime)...

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