CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for If G (X) is a Decreasing Function On R And F(X) = Tan−1 [G (X)]. State Whether F(X) is Increasing Or Decreasing On R ? - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

If g (x) is a decreasing function on R and f(x) = tan−1 [g (x)]. State whether f(x) is increasing or decreasing on R ?

Solution

\[\text { Given }:g\left( x \right)\text {  is decreasing on R }.\]

\[ \Rightarrow x_1 < x_2 \]

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

\[ \text {Applying tan}^{- 1} \text { on both sides, we get }\]

\[ \Rightarrow \tan^{- 1} \left\{ g\left( x_1 \right) \right\} > \tan^{- 1} \left\{ g\left( x_2 \right) \right\}\]

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

\[\text { Thus },\]

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

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

  Is there an error in this question or solution?

APPEARS IN

Solution for question: If G (X) is a Decreasing Function On R And F(X) = Tan−1 [G (X)]. State Whether F(X) is Increasing Or Decreasing On R ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
S
View in app×