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If `f,g: RvecR` are defined respectively by `f(x)=x^2+3x+1,g(x)=2x-3,` find fog (ii) gof (iii) fof (iv) gog.

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Given,
` f(x) = x2 + 3x + 1, g (x) = 2x – 3`
(i) `fog = f(g(x)) `
`= f(2x – 3)`
`= (2x – 3)2 + 3(2x – 3) + 1 `
`= 4x2 + 9 – 12x + 6x – 9 + 1 `
`= 4x2 – 6x + 1`
(ii)` gof = g(f(x)) `
...
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