RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 4 of Exercise 17.1

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4

Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R.

we have,

f(x) = ax + b, a < 0


let x1,x2 R and x1 > x2


ax1 < ax2 for some a > 0


ax1 + b< ax2 + b for some b


f(x1) < f(x2)


Hence, x1 > x2 f(x1) < f(x2)


So, f(x) is decreasing function of R


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