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Find the Inverse Function of F f(x)=3x−2x+5f ( x ) = \frac { 3 x - 2 } { x + 5 }

Question 288

Multiple Choice

Find the inverse function of f. State the domain and range of f.
- f(x) =3x−2x+5f ( x ) = \frac { 3 x - 2 } { x + 5 }


A) f−1(x) =x+53x−2\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 5 } { 3 \mathrm { x } - 2 } ; domain of f:{x∣x≠−5}\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } \neq - 5 \} ; range of f:{y∣y≠23}\mathrm { f } : \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 2 } { 3 } \right\}

B) f−1(x) =5x+23+x\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 2 } { 3 + \mathrm { x } } ; domain of f:{x∣x≠5}\mathrm { f } : \{ \mathrm { x } \mid \mathrm { x } \neq5 \} ; range of f:{y∣y≠3}\mathrm { f } : \{ \mathrm { y } \mid \mathrm { y } \neq 3 \}

C) f−1(x) =3x+2x−5f ^ { - 1 } ( x ) = \frac { 3 x + 2 } { x - 5 } ; domain of f:{x∣x≠−5}f : \{ x \mid x \neq - 5 \} ; range of f:{y∣y≠5}f : \{ y \mid y \neq 5 \}

D) f−1(x) =5x+23−xf ^ { - 1 } ( x ) = \frac { 5 x + 2 } { 3 - x } ; domain of f:{x∣x≠−5}f : \{ x \mid x \neq - 5 \} ; range of f:{y∣y≠3}f : \{ y \mid y \neq 3 \}

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