- Difficulty
- Standard
- Suggested time
- 3 min
- Marks
- 2
Functions, graphs and inverses practice question 8
Let . Find .
What does mean in terms of itself? Decide that before reaching for a formula for the inverse.
is the input that sends to 1. You do not need a formula for : solve .
Clear the denominator: .
A number, as a fraction or a decimal.
Theory UBC Math 100 §4.6CLP-1 §0.6Key results
Worked solution
Strategy
The value of an inverse function at 1 is whichever x has f(x) = 1. Solve that equation directly instead of inverting the whole formula.
Working
f⁻¹(1) = x exactly when f(x) = 1.
Multiply through by x + 2, which is not zero for the solution.
Check: f(3/2) = (9/2 − 1)/(3/2 + 2) = (7/2)/(7/2) = 1.
Answer
The answer is three halves.
Check
f(1.5) = 3.5/3.5 = 1, so f does send 1.5 to 1.
Where this goes wrong
Computing f(1) = 2/3 instead. f⁻¹(1) asks which input gives output 1, not what f does to the input 1.
Try a similar question
Let . Find without finding a formula for .Saved in this browser only.