Answered

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If \( f(x) = \frac{2x - 3}{5} \), which of the following is the inverse of \( f(x) \)?

A. \( f^{-1}(x) = \frac{3x + 2}{5} \)

B. \( f^{-1}(x) = \frac{3x + 5}{2} \)

C. \( f^{-1}(x) = \frac{2x + 3}{5} \)

D. [tex]\( f^{-1}(x) = \frac{5x + 3}{2} \)[/tex]

Sagot :

GinnyAnswer
To determine the inverse of the function \( f(x) = \frac{2x - 3}{5} \), we need to follow these steps:

1. Replace \( f(x) \) with \( y \):
[tex]\[ y = \frac{2x - 3}{5} \][/tex]

2. Interchange \( x \) and \( y \):
[tex]\[ x = \frac{2y - 3}{5} \][/tex]

3. Solve this equation for \( y \):
[tex]\[ x = \frac{2y - 3}{5} \][/tex]
To solve for \( y \), we first eliminate the fraction by multiplying both sides by 5:
[tex]\[ 5x = 2y - 3 \][/tex]

4. Isolate \( y \):
[tex]\[ 5x + 3 = 2y \][/tex]
[tex]\[ y = \frac{5x + 3}{2} \][/tex]

Therefore, the inverse function is:
[tex]\[ f^{-1}(x) = \frac{5x + 3}{2} \][/tex]

Based on the given choices, the correct answer is:
D. [tex]\( f^{-1}(x) = \frac{5x + 3}{2} \)[/tex]
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