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)

Question

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)

myininaya · Answer

f(x)=-1 is not 1 to 1 because it is a constant

myininaya · Answer

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 · Answer

so H(0)=-2
therefore 
H inverse of (-2)=0

anonymous · Answer

Thank so much. How do I sketch these?  Any idea?

myininaya · Answer

you just plug in points

anonymous · Answer

So, (A) would just be a line right? Straight across on the x-axis?

anonymous · Answer

I do not know which points to graph

myininaya · Answer

it would be a horizontal line going through y axis at y=-1

myininaya · Answer

for B just choose random points on both sides of 0 and including 0