A function is one-to-one if it never takes the same value twice. f(x) = 2x + 3 and f(x) = e^x are one-to-one.
Questions & Step-by-step Solutions
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Q
Q: Which of the following is a one-to-one function?
Solution: A function is one-to-one if it never takes the same value twice. f(x) = 2x + 3 and f(x) = e^x are one-to-one.
Steps: 6
Step 1: Understand what a function is. A function takes an input (x) and gives an output (f(x)).
Step 2: Learn what a one-to-one function means. A one-to-one function is a function where each output value is unique; no two different inputs give the same output.
Step 3: Check the first function, f(x) = 2x + 3. For any two different inputs, the outputs will also be different. This means it is a one-to-one function.
Step 4: Check the second function, f(x) = e^x. The exponential function also gives different outputs for different inputs, so it is also a one-to-one function.
Step 5: If a function can give the same output for different inputs, it is not one-to-one. For example, f(x) = x^2 is not one-to-one because both 2 and -2 give the same output (4).
Step 6: Conclude that f(x) = 2x + 3 and f(x) = e^x are both one-to-one functions.
