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If f and g are two real valued functions...

If f and g are two real valued functions defined as f(x) =2x +1 and `g (x) =x^(2) +1` then find
(i) f+g (ii) f-g (iii) fg (iv) `(f)/(g)`

Text Solution

Verified by Experts

We have `f(x)=2x+1 and g(x) =x^(2) +1`
(i) (f+g)(x)=f(x)-g(x)
`=2x+1+x^(2)+1=x^(2)+2x+2`
(ii) `(f-g)(x)=f(x)-g(x)=(2x+1)-(x^(2)+1)`
`=2x+1-x^(2)-1=2x-x^(2)=x(2-x)`
(iii) `(fg) (x) =f(x) * g(x)=(2x+1) (x^(2)+1)`
`=2x ^(3)+2x+x^(2)+1=2x^(3)+x^(2)+2x+1`
(iv) `(f)/(g) (x) =(f(x))/(g(x)) =(2x+1)/(x^(2)+1)`
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