15Twilight
Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Given the function f(x)=0.5(3)^x, what is the value of f^-1(7)?

Sagot :

[tex]f\left( x \right) =\frac { 1 }{ 2 } \cdot { 3 }^{ x }\\ \\ \frac { 1 }{ 2 } \cdot { 3 }^{ x }=y[/tex]

[tex]\\ \\ 2\cdot \frac { 1 }{ 2 } \cdot { 3 }^{ x }=2\cdot y\\ \\ { 3 }^{ x }=2y\\ \\ \log _{ 3 }{ \left( 2y \right) } =x[/tex]

[tex]\\ \\ \therefore \quad { f }^{ -1 }\left( x \right) =\log _{ 3 }{ \left( 2x \right) }[/tex]

[tex]\\ \\ \therefore \quad { f }^{ -1 }\left( 7 \right) =\log _{ 3 }{ \left( 2\cdot 7 \right) } =\log _{ 3 }{ 14 } [/tex]

there once was a ship called the billy of tea

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.