APFIVE Inverse Function Composition Property
Which of the following correctly demonstrates that the composition of a function and its inverse results in the identity function?
| x | $$f(x)=2x+1$$ | $$f^{-1}(x)=\frac{x-1}{2}$$ |
|---|---|---|
| 3 | 7 | 3 |
| 5 | 11 | 5 |
A
For $$f(x)=2*x+1$$ and $$g(x)=\frac{x}{2}+1$$, the composite function does not return the original input.
B
For $$f(x)=2*x+1$$, if one incorrectly computes $$f(f^{-1}(x))=\frac{x-1}{2}+1$$, it fails to produce the identity function.
C
For $$f(x)=2*x+1$$ with inverse $$f^{-1}(x)=\frac{x-1}{2}$$, the composition $$f(f^{-1}(x))=x$$, which shows the inverse property.
D
For $$f(x)=2*x+1$$ with a mistakenly defined inverse $$g(x)=2*x-1$$, the composition does not yield the identity function.
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