✗ Forgetting to swap x and y
✓ Always swap before rearranging
This is the crucial step that "undoes" the function
✗ Not verifying your answer
✓ Check that f(f⁻¹(x)) = x
Verification confirms you've done it correctly
✗ Confusing f⁻¹(x) with 1/f(x)
✓ f⁻¹ means inverse, not reciprocal
Inverse function ≠ reciprocal function
This exam tips covers Common Mistakes to Avoid within Inverse Functions for GCSE Mathematics. Revise Inverse Functions in Algebra for GCSE Mathematics with 8 exam-style questions and 4 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 7 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
Practice questions for Inverse Functions
What does f⁻¹(x) represent?
Explain why the function f(x) = x² (for all real x) does not have an inverse function over its full domain.
Quick recall flashcards
What does f⁻¹ notation mean?
Inverse function (NOT 1/f). It's the function that undoes f, not the reciprocal
What is an inverse function?
A function that undoes what the original function does. f⁻¹(x) reverses the operation of f(x)