Functions
Functional equation with reciprocal input
nta_pyq_2025_apr
Grade 12
Question:
Let f be a function such that f$(x) + 3f$( 24$) = 4x$, x$\ne$0 . Then f$(3) + f$(8) is equal to x
Step-by-Step Solution
Key Concept: Write the given equation with the transformed input and solve the resulting simultaneous equations for the function value.
f$(x) + 3f$( 24$) = 4x$x (1) Put$x = 3$f$(3) + 3f$$(8) = 12$Put$x = 8$f$(8) + 3f$$(3) = 32$Add both 4(f$(3) + f$$(8)) = 44$f$(3) + f$$(8) = 11$
Correct Answer: 1