CAT 2024 Functions Question (Hard)

Question

For any non-zero real number , let . Then, the sum of all possible values of for which , is

Accepted Answer

Step 1 We are given a functional equation We are also told to find the sum of all possible values of such that . Step 2 Substitute into the functional equation Now, solve for Step 3 Now reverse the roles use the functional equation with replaced by . So We already have , so Step 4 Now equate the two

CAT 2024

Quantitative

Functions

Hard

For any non-zero real number $x$ , let $f(x)+2 f\left(\frac{1}{x}\right)=3 x$ . Then, the sum of all possible values of $x$ for which $f(x)=3$ , is

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