Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Evaluate function notation.
- Derive an inverse linear rule.
- Check a conversion by a round trip.
Before you start
Multiply fractions and decimals; solve a linear equation for a chosen variable.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
The temperature conversion rule is F(C) = (9/5)C + 32. What Fahrenheit reading corresponds to 20°C, and how can you recover Celsius from a Fahrenheit reading?
Why this math matters
A function maps each allowed input to one output. An inverse reverses that mapping when different inputs have different outputs. Temperature conversion makes the order of operations visible because the reverse rule must undo them in reverse order.
Set up the model
A useful answer starts with clear assumptions:
- C and F are numerical readings on the Celsius and Fahrenheit scales.
- The exercise converts readings, not physical quantities of heat.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Run a temperature-conversion function forwards and backwards
PausedQuestion: Start with the question. Paused.
Question
Start with the question
The temperature conversion rule is F(C) = (9/5)C + 32. What Fahrenheit reading corresponds to 20°C, and how can you recover Celsius from a Fahrenheit reading?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Evaluate the forward rule
F(20) = (9/5)(20) + 32 = 36 + 32 = 68
The notation F(20) means the output at input twenty. It does not mean F multiplied by twenty.
Reverse the operations
F − 32 = (9/5)C; C = (5/9)(F − 32)
Undo the final addition first, then undo multiplication by 9/5 using its reciprocal. Parentheses preserve that order.
Check the round trip
C(68) = (5/9)(68 − 32) = (5/9)(36) = 20
Returning to the starting reading confirms the inverse calculation. Each real Celsius input produces a different Fahrenheit output.
The result
20°C corresponds to 68°F; the reverse rule is C(F) = (5/9)(F − 32).
A temperature increase of 10°C corresponds to an increase of 18°F, not 50°F. The added thirty-two belongs to converting a reading, while it cancels when comparing two readings.
Common mistakes to catch
- Subtract thirty-two before multiplying by 5/9 in the inverse rule.
- An inverse function is not the reciprocal of the original function's output.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Convert 30°C to Fahrenheit.
Show a hint
Multiply thirty by 9/5, then add thirty-two.
Reveal answer and explanation
86°F
(9/5)(30) + 32 = 54 + 32 = 86.
Practice 2
Convert 50°F to Celsius.
Show a hint
Use the reverse rule and group the subtraction.
Reveal answer and explanation
10°C
(5/9)(50 − 32) = (5/9)(18) = 10. Converting back gives 18 + 32 = 50°F.
Take the idea with you
For a two-operation conversion, describe the forward operations aloud and then list their inverses in reverse order.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
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