anonymous
  • anonymous
I'm lost with 2 different problems and just can't seem to get it. Determine whether the given function f(x) is one-to-one. If it is, find its inverse f^-1(x), and sketch the graphs of y=f(x) and y=f^-1(x) on the same coordinate axes. (A) f(x) = -1 (B) Let H(x) = 2x^3 + 5x-2. Find H^-1(-2)
Mathematics
chestercat
  • chestercat
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myininaya
  • myininaya
f(x)=-1 is not 1 to 1 because it is a constant
myininaya
  • myininaya
H(x)=2x^3+5x-2 is 1 to 1 if H inverse of (-2)=a then H(a)=-2 so we have H(a)=2a^3+5a-2=-2 2a^3+5a-2+2=-2+2 2a^3+5a=0 a(2a^2+5)=0 a=0
myininaya
  • myininaya
so H(0)=-2 therefore H inverse of (-2)=0

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anonymous
  • anonymous
Thank so much. How do I sketch these? Any idea?
myininaya
  • myininaya
you just plug in points
anonymous
  • anonymous
So, (A) would just be a line right? Straight across on the x-axis?
anonymous
  • anonymous
I do not know which points to graph
myininaya
  • myininaya
it would be a horizontal line going through y axis at y=-1
myininaya
  • myininaya
for B just choose random points on both sides of 0 and including 0

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