We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
398
2
avatar

1. Let $f(x) = Ax - 2B^2$ and $g(x) = Bx$, where $B \neq 0$. If $f(g(1)) = 0$, what is $A$ in terms of $B$?

2. Suppose that $f$ is a function and $f^{-1}$ is the inverse of $f$. If $f(1)=2$, $f(2) = 6$, and $f(3)=5$, then what is $f^{-1}(f^{-1}(6))$?

 Jul 16, 2018
 #1
avatar+22550 
+2

1. Let $f(x) = Ax - 2B^2$ and $g(x) = Bx$, where $B \neq 0$. If $f(g(1)) = 0$, what is $A$ in terms of $B$?

2. Suppose that $f$ is a function and $f^{-1}$ is the inverse of $f$. If $f(1)=2$, $f(2) = 6$, and $f(3)=5$, then what is $f^{-1}(f^{-1}(6))$?

 

 

\(\begin{array}{|lrcll|} \hline x = 1 : & g(x) &=& g(1) \\ & g(1) &=& B\cdot 1 \\ & g(1) &=& B \\\\ & f(g(1)) &=& f(B) \\ x=B: & f(B) &=& A\cdot B - 2B^2 \\ f(B) = 0: & A\cdot B - 2B^2 &=& 0 \\ & A\cdot B&=& 2B^2 \\ & A &=& \dfrac{2B^2}{B} \quad & | \quad B \ne 0~ ! \\ &\mathbf{ A }& \mathbf{=}& \mathbf{ 2B } \\ \hline \end{array}\)

 

laugh

 Jul 17, 2018
 #2
avatar+22550 
+2

1. Let $f(x) = Ax - 2B^2$ and $g(x) = Bx$, where $B \neq 0$. If $f(g(1)) = 0$, what is $A$ in terms of $B$?
2. Suppose that $f$ is a function and $f^{-1}$ is the inverse of $f$. If $f(1)=2$, $f(2) = 6$, and $f(3)=5$, then what is $f^{-1}(f^{-1}(6))$?

 

\(\begin{array}{|r|r|r|r|} \hline x & f(x) \\ \hline 1 & 2 & f(1) = 2 & f^{-1}(2) = 1 \\ 2 & 6 & f(2) = 6 & f^{-1}(6) = 2 \\ 3 & 5 & f(3) = 5 & f^{-1}(5) = 3 \\ \hline f^{-1}(x) & x \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline f^{-1}(6) &=& 2 \\ f^{-1}(f^{-1}(6)) &=& f^{-1}(2) \\ &=& 1 \\\\ \mathbf{f^{-1}(f^{-1}(6))}& \mathbf{=}& \mathbf{1} \\ \hline \end{array}\)

 

 

laugh

 Jul 17, 2018

8 Online Users

avatar