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Let f(x)=x^2and g(x) = 2x + 1be two r...

Let `f(x)=x^2`and `g(x) = 2x + 1`be two real functions. find `(f +g)(x)`, `(f-g)(x)`, `(fg)(x)`, `(f/g)(x)`.

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Here, `f(x) = x^2` and `g(x) = 2x+1`
`(f+g)(x) = f(x)+g(x) = x^2+2x+1`
`(f-g)(x) = f(x)-g(x) = x^2-2x-1`
`(fg)(x) = f(x)g(x) = x^2(2x+1) = 2x^3+x^2`
`(f/g)(x) = f(x)/g(x) = x^2/(2x+1)`
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NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Define the function f : R ->R by y = f(x) = x^2, x in R. Complete ...

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  2. Let N be the set of natural numbers and the relation R be defined on ...

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  3. Let f(x)=sqrt(x)and g(x) = xbe two functions defined over the set of ...

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  4. Let f(x)=x^2and g(x) = 2x + 1be two real functions. find (f +g)(x),...

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  5. Define the real valued function f : R {0} ->Rdefined by f(x)=1/x,...

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  6. Draw the graph of the function f : R-> Rdefined by f(x)=x^3, x in R...

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  7. Let R be a relation from Q to Q defined by R={(a,b):a,b in Q and a,b i...

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  8. Let R be the set of real numbers. Define the real function f : R ->Rb...

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  9. If (x + 1, y - 2) = (3, -1), find the values of x and y.

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  10. Let A= {1, 2, 3}, B = {3, 4}and C = {4, 5, 6}. Find(i) A xx(B nnC...

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  11. If P = {a , b , c}and A xxB = {(p , q), (p , r), (m , q), (m , r)}Q = ...

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  12. If R is the set of all real numbers, what do the cartesian products R...

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  13. If P = {1, 2}form the set P xxP xxP.

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  14. The function f is defined by f(x) ={[1-x \ x<0], [1 \ \ \ \ \ \ \ \ ...

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  15. Find the domain of the function f(x) =(x^2-3x+5)/(x^2-5x+4).

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  16. Let f = {(1, 2), (2, 3), (0, -1), ( -1, -3)} be a linear function ...

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  17. If A xxB = {(p , q), (p , r), (m , q), (m , r)}, find A and B.

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  18. Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x...

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  19. The Fig 2.6 shows a relation between the sets P and Q. Write this rel...

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  20. Let A = {1, 2}and B = {3, 4}. Find the number of relations from A to...

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