[tex]\large{\mathbb{\underline{ANSWER:}}}[/tex]
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[tex]{ \underline{ \boxed{ \purple{ \tt{ {f - }^{1}(x) = \frac{1 + 4 \times }{ - 2 + 3 \times } }}}}}[/tex]
Domain:
[tex] \tt \large ( - \infty \frac{4}{3} ) \cup ( \frac{2}{3 } \infty ) [/tex]
Range:
[tex] \tt \large( - \infty \frac{4}{3 }) \cup ( \frac{4}{3} \infty )[/tex]
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[tex]\large{\mathbb{\underline{EXPLANATION:}}}[/tex]
Rewrite the function using
[tex] \tt \large \: y:y = \frac{2 x + 1}{3 x - 4} [/tex]
Interchange the positions of x and y in the function:
[tex] \tt \large x = \frac{2y + 1}{3y - 4} [/tex]
Isolate the dependent variable:
[tex] \tt \large \: y \frac{1 + 4 x }{ - 2 + 3 x} [/tex]
Find the inverse function:
[tex] \tt \large {f - }^{1} (x) = \frac{1 + 4 x}{ - 2 + 3x} [/tex]
Get the result:
[tex] \tt \large{f}^{1} (x) = \frac{1 + 4x}{ - 2 + 3x} [/tex]
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#CarryOnLearning
[tex]\large\boxed {\begin{array}{}{{\tt\red{₰}}} \end{array}}[/tex]
