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If f(x)=4x-x^2, x in R , then write the...

If `f(x)=4x-x^2, x in R ,` then write the value of `f(a+1)-f(a-1)dot`

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To solve the problem, we need to find the value of \( f(a+1) - f(a-1) \) given the function \( f(x) = 4x - x^2 \). ### Step 1: Calculate \( f(a+1) \) Using the function definition: \[ f(a+1) = 4(a+1) - (a+1)^2 \] Expanding this: ...
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RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Write the range of the real function f(x)=|x|dot

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  2. If f(x)=1-1/x then write the value of f(f(1/x))dot

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  3. If f(x)=4x-x^2, x in R , then write the value of f(a+1)-f(a-1)dot

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  4. If f,\ g,\ h are real functions given by f(x)=x^2,g\ (x)=tanx\ a n d\ ...

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  5. Write the domain and range of function f(x) given by f(x)=1/(sqrt(x-[x...

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  6. Write of the domain and range of f(x)=sqrt(x-[x])dot

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  7. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x).

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  8. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

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  9. Find the values of x for which the functions f(x)=3x^2-1 and g(x)=3+x ...

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  10. If f(x)="cos"((log)e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value ...

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  11. Let f(x)=|x-1|dot Then (a)f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c)f(...

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  12. If A={1,2,3},\ B={x , y} , then the number of functions that can be de...

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  13. If x!=1\ a n d\ f(x)=(x+1)/(x-1) is a real function, then f(f(f(2))) ...

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  14. If f: R->R : x!=0,\ -4lt=xlt=4 and f: A->A be defined by f(x)=(|x|)/x ...

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  15. If f: RrarrR and g: RrarrR are defined by f(x)=2x+3a n dg(x)=x^2+7, th...

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  16. If f: [-2, 2] -> R is defined by f(x)={-1,for -2<=x<=0 , then x...

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  17. If f(x)=64x^3+1/x^3 and alpha,beta are the roots of 4x+1/x=3. Then,f(a...

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  18. The domain of the function f(x)=sqrt(2-2x-x^2) is [-sqrt(3),\ sqrt(3)...

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  19. The domain of the function f(x)=sqrt[((x+1)(x-3))/(x-2)] is [-1,2)uu[3...

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  20. The domain of the function f(x)=sqrt(((x+1)(x-3))/(x-2)) is [-1,2)uu[3...

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