One-to-One Functions and Inverses

Only some functions can be undone.

12 problems · about 22 minutes · TEKS P.2.B, TEKS P.2.C

NameDate

Figure — use these to answer the problems

Set the slope to 1 and the intercept to 0 to draw y = x, the mirror line every inverse reflects across.

y = x

Slope1

y-intercept0

Figure 1

Straightforward practice. Get the method working first.

5 problems

(2, 11) lies on f. What is f⁻¹(11)?
Answer
2
Why must a function be one-to-one to have an inverse?
- Otherwise one output would need to map back to two inputs.
- Otherwise the graph would be a curve.
f(x) = 2x + 3. What is f⁻¹(9)?
Answer
(5, 2) lies on f⁻¹. What is f(2)?
Answer
f(x) = x³. What is f⁻¹(27)?
Answer

The same ideas with more to keep track of.

3 problems

The range of f is y ≥ 4. What is the smallest value in the domain of f⁻¹?
Answer
f(x) = x² on x ≥ 0. What is f⁻¹(49)?
Answer
Which line does the graph of an inverse reflect across? Enter 1 for y = x, or 2 for the x-axis.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Which functions are one-to-one over all real numbers?
- f(x) = 3x − 7
- f(x) = x³ + 1
- f(x) = x⁴
- f(x) = |x| + 2
- Tick every box that applies.
f(x) = (x − 1) ÷ 4. What is f⁻¹(2)?
Answer
The Point
The point (3, 8) lies on f. What is the x-coordinate of the matching point on f⁻¹?
Answer
12
The Test
Which function fails the horizontal line test?
- f(x) = x²
- f(x) = 2x + 1
- f(x) = x³