The Function F Is One-To-One $$f ( x ) = \sqrt { 3 - 4 x }$$

question 151

Multiple Choice

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder
notation.
- $$f ( x ) = \sqrt { 3 - 4 x }$$

• A) \(\begin{array}{l}
• f(x): D=\left\{x \mid x \leq \frac{3}{4}\right\}, R=\{y \mid y \geq 0\} \\
• f^{-1}(x): D=\{x \mid x \geq 0\}, R=\left\{y \mid y \leq \frac{3}{4}\right\}
• \end{array}\)
• B)
• \( f(x): D=\left\{x \mid x \leq \frac{3}{4}\right\}, R \) is all real numbers;
• \( \mathrm{f}^{-1}(\mathrm{x}): \mathrm{D} \) is all real numbers, \( R=\left\{y \mid y \leq \frac{3}{4}\right\} \)
• C) \(\begin{array}{c}
• f(x): D=\{x \mid x \geq 0\}, R=\{y \mid y \geq 0\} \\
• f^{-1}(x): D=\left\{x|x \geq 0\rangle, R=\left\{y \mid y \geq \frac{3}{4}\right\}\right.
• \end{array}\)
• D)\[
• f(x): D=\left\{x \mid x \leq \frac{3}{4}\right\}, R=\{y \mid y \leq 0\}
• \]
• \( f^{-1}(x): D \) is all real numbers, \( R=\left\{y \mid y \leq \frac{3}{4}\right\} \)

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