SOLUTION: a) For the given functions 𝑓(𝑥)= x/x-1 and g(x)=-4/x ,find the domain of the composite functions 𝑓o𝑔 and 𝑔o𝑓. b) Is 𝑓(𝑥)=x^3 invertible? Explain wi

Question 1189264: a) For the given functions 𝑓(𝑥)= x/x-1 and g(x)=-4/x ,find the domain of the
composite functions 𝑓o𝑔 and 𝑔o𝑓.
b) Is 𝑓(𝑥)=x^3 invertible? Explain with reason.
If 𝑓(𝑥) is invertible, find the inverse of 𝑓(𝑥). Also, graph 𝑓 and 𝑓^-1 on the
same coordinate axes.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
a) For the given functions and ,find the domain of the
composite functions o and o.
o
o
o
o
o
domain: exclude that makes denominator equal to zero which is
so, domain is { element : }
o
o
o
o
domain:{ element : }

b) Is invertible? Explain with reason.
yes, is invertible
reason: pass a horizontal line test
If we take a horizontal line and slide it up and down the graph, it only ever intersects the function in one spot! This means that each output corresponds with exactly one input. In other words, each input has a unique output. The function is invertible.

If is invertible, find the inverse of . Also, graph and on the same coordinate axes.
............recall
..........swap variables
.........solve for

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