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Let f and g real functions defined by f(...

Let `f` and `g` real functions defined by `f(x) =2x +1` and `g (x) = 4x-7`.
(i) For what real number `x,f(x)=g(x)?`
(ii) `x,f(g) lt g(x)`?

Text Solution

Verified by Experts

We have, f(x)=2x+1 and g(x) =4x-7
(i) `:. f(x) =g(x)`
`rArr 2x+1=4x-7rArr2x=8`
`:. x=4`
(ii) `:. f(x) ltg(x)`
`rArr 2x+1lt 4x-7`
`rArr 2x-4x+1lt 4x -7-4x`
`rArr -2x+1 lt-7`
`rArr 2x lt -7 -1`
`rArr -2xlt-8`
`rArr (-2x)/(-2) gt (-8)/(-2)`
`:. x gt 4`
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