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