The Total solution for NCERT class 6-12
Prove that f(x) =ax + b, where a, b are constants and a < 0 is a decreasing function on R.
Given,
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