SOLUTION: for the function g(x)=-1+log2(x-5) (i) find g^-1(x) (ii) sketch the graph of g(x) and g^-1(x) on the same coordinate axes showing the asymptotes and intercepts

Algebra ->  Functions -> SOLUTION: for the function g(x)=-1+log2(x-5) (i) find g^-1(x) (ii) sketch the graph of g(x) and g^-1(x) on the same coordinate axes showing the asymptotes and intercepts      Log On


   

Question 1084542: for the function g(x)=-1+log2(x-5)
(i) find g^-1(x)
(ii) sketch the graph of g(x) and g^-1(x) on the same coordinate axes showing the asymptotes and intercepts
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
for the function g(x)=-1+log2(x-5)
(i) find g^-1(x)
1st:: Interchange x and y to get x = -1+log2(y-5)
2nd:: Solve for "y"::
log2(y-5) = x+1
y-5 = 2^(x+1)
Ans:: g^-1(x) = 2^(x+1)+5
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(ii) sketch the graph of g(x) and g^-1(x) on the same coordinate axes showing the asymptotes and intercepts
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Asymptotes and intercepts::
For g(x) = -1+log2(x-5)
Asymptote:: x = 5
x-intercept:: Solve log2(x-5) = 1 ; x-5 = 2 ; x = 7
y-int:: none
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For g^-1(x) = 2^(x+1)+5
Asymptote:: y = 5
x-intercept:: none
y-intercept:: y = 7
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Cheers,
Stan H.
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