Question

select the correct answer.
find the inverse of function f.
$f(x) = \frac{1}{2}x + 7$
\\(\bigcirc\\) a. \\(f^{-1}(x) = 2x - 7\\)
\\(\bigcirc\\) b. \\(f^{-1}(x) = 2x - 14\\)
\\(\bigcirc\\) c. \\(f^{-1}(x) = x - 7\\)
\\(\bigcirc\\) d. \\(f^{-1}(x) = 2x + \frac{1}{7}\\)

Explanation:

Step1: Replace \( f(x) \) with \( y \)

\( y = \frac{1}{2}x + 7 \)

Step2: Swap \( x \) and \( y \)

\( x = \frac{1}{2}y + 7 \)

Step3: Solve for \( y \)

Subtract 7 from both sides: \( x - 7 = \frac{1}{2}y \)
Multiply both sides by 2: \( y = 2(x - 7) = 2x - 14 \)

Step4: Replace \( y \) with \( f^{-1}(x) \)

\( f^{-1}(x) = 2x - 14 \)

Answer:

B. \( f^{-1}(x) = 2x - 14 \)