यदि `f,g:R rarr R` दो फलन हैं , जो निम्न प्रकार परिभाषित हैं -
`f(x)=sqrt(x-1), g(x)=sqrt(4-x^(2))` तो ज्ञात कीजिए ।
`(i) f+g " " (ii) g+f " " (iii) f-g " " (iv) g-f " " `
(v) `fg" " (vi) gf " " (vii) f//g " " (viii) g//f`

Answer

`(i) sqrt(x-1)+sqrt(4-x^(2)) (ii) sqrt(4-x^(2))+sqrt(x-1) (iii) sqrt(x-1)-sqrt(4-x^(2)) (iv) sqrt(4-x^(2))-sqrt(x-1) (v) sqrt((x-1)(4-x^(2))) (vi) sqrt((4-x^(2))(x-1)) (vii) sqrt((x-1)/(4-x^(2))) (viii) sqrt((4-x^(2))/(x-1))`

Explanation

`f(x)=x^(2)-3x+2 rArr f[f(x)]=f[x^(2)-3x+2]`
`rArr (x^(2)-3x+2)^(2)-3(x^(2)-3x+2)+2]=x^(4)-6x^(3)+10x^(2)-3x+6`