Inverse Functions, step by step
An inverse function reverses what the original did. Its graph is the reflection in y = x.
- REPLACE f(x) WITH yJust notation, to make the swap readable.
- SWAP x AND yThis is the actual inversion.
- SOLVE FOR yRearrange until y is alone.
- CHECKf(f⁻¹(x)) should give back x.
worked
- f(x) = 2x + 3 → y = 2x + 3 → x = 2y + 3
- y = (x − 3)/2, so f⁻¹(x) = (x − 3)/2
f⁻¹ does not mean 1/f. It means the inverse function — a completely different thing.
Questions about the Inverse Functions poster
- What’s on the Inverse Functions poster?
- 4 numbered steps, with a full worked run-through. An inverse function reverses what the original did. Its graph is the reflection in y = x. REPLACE f(x) WITH y — Just notation, to make the swap readable.; SWAP x AND y — This is the actual inversion.; SOLVE FOR y — Rearrange until y is alone.; CHECK — f(f⁻¹(x)) should give back x.. f⁻¹ does not mean 1/f. It means the inverse function — a completely different thing.
- Who is the Inverse Functions poster for?
- Inverse Functions is filed under 10th Grade (ages 15–16), so it matches what that year asks a child to remember. It is equally useful to an older student revisiting math, and to the parent or teacher answering the question at the kitchen table.
- When should you use the Inverse Functions poster?
- Swap x and y, then solve for y. That is the entire procedure. A wall chart earns its place by being glanceable from where the work is happening, so Inverse Functions belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Inverse Functions?
- Sequences and Series, Completing the Square and Complex Numbers sit alongside Inverse Functions in the 10th Grade set. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Sequences and SeriesCompleting the SquareComplex Numbers
- Is the Inverse Functions poster free to download and print?
- Yes. Inverse Functions downloads as a free PDF with no account, no email and no watermark, like everything else in the 10th Grade set. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Inverse Functions poster print at?
- Inverse Functions is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Inverse Functions loses nothing.Printing guide
Related posters
Charts that sit alongside Inverse Functions on the same wall.
Browse every 10th Grade poster, or start from the full catalogue.