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Functions (Advanced) formula sheet

Every formula in the Functions (Advanced) chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 15 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Domain of combined expressions

Variable base and nested logs
4× asked, last 2025
log⁡g(x)f(x): f>0, g>0, g≠1log⁡au>k  ⟺  u>ak (a>1)\begin{aligned}&\log_{g(x)}f(x):\ f>0,\ g>0,\ g\ne1\\&\log_au>k\iff u>a^k\ (a>1)\end{aligned}
0<a<10<a<1 flips it. Work from the outside in: log⁡4log⁡3log⁡7u\log_4\log_3\log_7u needs u>7u>7.
sin⁻¹ of a rational function
7× asked, last 2025
−1≤pq≤1  ⟺  p−qq≤0 and p+qq≥0-1\le\frac pq\le1\iff\frac{p-q}q\le0\ \text{and}\ \frac{p+q}q\ge0
Sign charts; q≠0q\ne0. Never cross-multiply by an unknown sign. Domain from the original expression.

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Practise Functions (Advanced)

13 more formulas in 4 topics

Range of a function; Composite and inverse functions; Even, odd, periodic functions and graphs; and Functional equations. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Range of a function

  • Discriminant method2×
  • Monotonic functions2×
  • Bounds4×

Composite and inverse functions

  • Inverse function5×
  • Values and slopes of the inverse4×

Even, odd, periodic functions and graphs

  • Even and odd1×
  • Periods
  • Graph transformations

Functional equations

  • Additive8×
  • Exponential8×
  • Power, log, cosine types5×
  • f(x) and f(1/x)7×
  • Pairing sums4×

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About 70 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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