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1.) Let f(x)=7x+5 and g(x)=x-1.  If h(x)=f(g(x)), then what is the inverse of h(x)?

 

2.) If the point (3,6) is on the graph of y=g(x), and h(x)=(g(x))^2 for all x, then there is one point that must be on the graph of y=h(x). What is the sum of the coordinates of that point?

 Mar 30, 2019
 #1
avatar+10536 
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1.) Let f(x)=7x+5 and g(x)=x-1.  If h(x)=f(g(x)), then what is the inverse of h(x)?

 

2.) If the point (3,6) is on the graph of y=g(x), and h(x)=(g(x))^2 for all x, then there is one point that must be on the graph of y=h(x). What is the sum of the coordinates of that point?

 

laugh

 Mar 30, 2019
 #2
avatar+6026 
0

another way of doing (1)

 

\(h(x)=f(g(x))\\ h^{-1}(x) = g^{-1}(f^{-1}(x))\)

 

\(f^{-1}(x) = \dfrac{x-5}{7}\\ g^{-1}(x) = x+1\\ g^{-1}(f^{-1}(x))=\dfrac{x-5}{7}+1 = \dfrac{x+2}{7}\)

.
 Mar 30, 2019

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