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If f,\ g,\ h are real functions defined ...

If `f,\ g,\ h` are real functions defined by `f=sqrt(x+1),\ g(x)=1/x\ a n d\ h(x)=2x^2-3,` then find the values of `(2fg+g-h)(1)\ a n d\ (2f+g-h)(1)dot`

Text Solution

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`f(x)` is defined for `x+1>=0`.
`x>=-1`
`x in [-1, oo]`
`g(x)` is defined for x != 0
`x in R-{0}` and `h(x)` is defined for all `x` such that `x in R`.
Thus domain `(f)` `cap` domain `(g)` `cap` domain `(h)` =`[-1, oo]-{0}`
`(2f+g-h):[-1, oo]-{0}->R` is given by:
`(2f+g-h)(x)=2f(x)+g(x)-h(x)` ...
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