CAT 2017 Functions Question (Medium)

Question

Let f x 2x 5 and g x 7 2x. Then f x g x f x g x if and only if

Accepted Answer

Step 1 Given Then, So, We are to find when Step 2 Note the points where and change sign when when Split into 3 intervals Case 1 So Set equal to 2 Case 2 , So Case 3 Then, , So Set equal to 2 Step 3 Thus, equality holds when , , and for all in between. Final Answer The equality holds if and only if

CAT 2017

Quantitative

Functions

Medium

$Let f(x) = 2x - 5 and g(x) = 7 - 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if$

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