General functions
Inverse functions worksheets
Identify inverse pairs or find inverse functions in twelve original questions. Practice linear functions and powers with explicit domains, exact radicals and worked answers.
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Logarithmic function inverses worksheets
Find inverses in logarithmic, exponential or mixed directions across six exact forms. Every problem prints the real domain needed for a single-valued inverse, with separate exact answer keys.
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Use the printed domain for the given function. Swap x and y, solve for y, and write the inverse with its domain. Keep the nonnegative branch for even roots.
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Reverse the rule. Carry the domain with it.
Choose any nonempty subset of six logarithmic forms, logarithmic or exponential prompts, and twelve or fourteen problems. Mixed sheets place logarithmic prompts first and exponential prompts second.
Each given function includes its real domain. Swap x and y, solve for y, then use the original range as the inverse domain. Signed scales and logarithm multipliers remain part of the exact inverse formula.
Even powers use the printed nonnegative branch. Depending on the affine constant and scale, an endpoint may be included, excluded or bound both sides of an interval. The key preserves exact rational, radical and logarithmic endpoints.
Learning objective
What this activity builds
Reverse logarithmic and exponential functions while carrying each restricted real domain to the inverse.
Worked example
Find the inverse of f(x) = log₂(3x² + 7) on x ≥ 0.
f⁻¹(x) = √((2^x − 7)/3), with domain [log₂(7), ∞).
The nonnegative branch makes the logarithmic function one-to-one. Its range begins at log₂(7), so that interval becomes the inverse domain.
Teaching notes
Make the practice count
- Swap the roles of x and y before isolating the output.
- Treat the given domain as part of the function.
- Use a principal nonnegative root for every even-power branch.
- Exchange the original domain and range to obtain the inverse range and domain.
- Keep signed input scales and logarithm multipliers attached during isolation.
- Check both compositions on the stated intervals.
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