`f(x)={:{(-1","," यदि " x le 0),( ax+b","," यदि "0ltxlt1),(1","," यदि "x gt 1):}` जहाँ a, b अचर हैं । फलन सर्वत्र सतत है । a का मान क्या है ?

Correct Answer - D
दिया है,`f(x)={:{(-1","," यदि " x le0),(ax+b","," यदि "0 lt x lt 1),(1","," यदि " x ge 1):}`
जहाँ, a तथा b अचर हैं तथा f(x) सभी जगह सतत है । चूँकि f(x) सभी जगह सतत है, इसलिए f, x=0 तथा x=1 पर भी सतत होगा ।
`=underset(xrarr0)limf(x)=underset(xrarr0^(-))limf(x)=f(0)`
तथा `underset(xrarr1^(+))limf(x)=underset(xrarr1^(-))limf(x)=f(1)`
अब, `underset( x rarr 0^(+))limf(x)=f(0)`
`rArr underset(hrarr0)lima(0+h)+b=-1 rArr b = - 1 `
तथा `underset(xrarr1^(-))limf(x)=f(1)`
`rArr underset(hrarr0)limf(1-h)=1`
`rArrunderset(hrarr0)lima(1-h)+b=1`
`rArr a+b=1`
`rArr a+(-1)=1 rArr a = 2 `