Q4 of 105 Page 17

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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