Question 714700: I need help asap!!! someone help!
Use the given function f to answer parts a) through f)below.
f(x)=1+log5(x+3)
a)the domain of f
b)graph f
c) from the graph, determine the range and any asymptotes of f.
d)find f^-1, the inverse of f
e)find the domain and range of f^-1
f)graph f^-1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! f(x)=1+log5(x+3)
a)the domain of f: (-3,∞)
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b)graph f
I don't have the means to graph it, but I can try to show you how to do it.
Start with the basic log5(x) basic curve which has an asymptote at x=0 or the y-axis and an
x-intercept at(1,0). Then move this curve 3 units left, placing the asymptote and x-intercept at
x=-3 and (-2,0), respectively. Lastly, bump the curve up one unit.
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c) from the graph, determine the range and any asymptotes of f. Range: (-∞,∞); asymptote:x=-3
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d)find f^-1, the inverse of f
y=1+log5(x+3)
interchange x and y, then solve for y
x=1+log5(y+3)
x-1=log5(y+3)
5^(x+1))=y+3
f^-1=5^(x+1)-3
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e)find the domain and range of f^-1: Range:(-3,∞); Domain:(-∞,∞)
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f)graph f^-1
curve has a horizontal asymptote at y=-3 and a y-intercept at (0,2)
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