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Maths Question 3 – JEE-MAIN 2025

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Let f be a function such that f(x)+3f(24x)=4x,x≠0. Then f(3)+f(8) is equal to

When dealing with functional equations involving x and a related term like c/x, a common strategy is to substitute specific values for x that relate the arguments.

Step 1: Set up equations for f(3) and f(8)✦ Active

The given functional equation is f(x)+3f(24x)=4x. We need to find f(3)+f(8). Let's substitute x=3 into the equation:

f(3)+3f(243)=4(3) f(3)+3f(8)=12(1)

Now, substitute x=8 into the original equation:

f(8)+3f(248)=4(8) f(8)+3f(3)=32(2)
Step 2: Solve the system of linear equations○ Expand

We have a system of two linear equations with f(3) and f(8) as variables:

f(3)+3f(8)=12(1) 3f(3)+f(8)=32(2)

To find f(3)+f(8), we can add Equation (1) and Equation (2) directly:

(f(3)+3f(8))+(3f(3)+f(8))=12+32
💡 Teacher's Secret Hint

Adding the equations is a more efficient method than solving for each variable individually if the sum is required.

Step 3: Calculate the sum f(3)+f(8)○ Expand

Combine like terms from the sum of the equations:

4f(3)+4f(8)=44

Factor out 4 from the left side:

4(f(3)+f(8))=44

Divide both sides by 4 to find the required sum:

f(3)+f(8)=444 f(3)+f(8)=11
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