CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Prove that F(X) = Ax + B, Where A, B Are Constants and a < 0 is a Decreasing Function on R ? - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

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

Solution

\[f\left( x \right) = ax + b\]

\[\text { Let }x_1 , x_2 \text { in R such that } x_1 < x_2 . \]

\[\text { Then },\]

\[ x_1 < x_2 \]

\[ \Rightarrow a x_1 > a x_2 (\because a<0)\]

\[ \Rightarrow a x_1 + b > a x_2 + b\]

\[ \Rightarrow f\left( x_1 \right) > f\left( x_2 \right)\]

\[\text { Thus }, x_1 < x_2 \]

\[ \Rightarrow f\left( x_1 \right) > f\left( x_2 \right), \forall x_1 , x_2 \in R\]

\[\text { So },f\left( x \right) \text { is decreasing on R } .\]

  Is there an error in this question or solution?
Solution for question: Prove that F(X) = Ax + B, Where A, B Are Constants and a < 0 is a Decreasing Function on R ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science
S
View in app×