we have,f(x) = ax + b, a > 0let 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 increasing function of R

Q. 35.0( 3 Votes )

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Class 12th RD Sharma - Volume 1 17. Increasing and Decreasing Functions

Answer :

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 increasing function of R

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