## anonymous 5 years ago for what type of function will {g(f(x))}and {f(g(x))} both equal to x? explain.

1. anonymous

When one is the inverse of the other.

2. anonymous

y

3. anonymous

Take the first case, g(f(x)). You take x and f maps it to f(x). You're wanting g now such that g will take that result and send it back to x (i.e. undo the operation). The function that will do that is the inverse of the original function.

4. anonymous

This is the definition of an inverse function.

5. anonymous

Example, $f(x)=e^x , g(x) = \ln x$then$f(g(x))=e^{\ln x}=x$by definition of logarithm, and$g(f(x))=\ln e^x = x \ln e = x$by log laws. The two functions,$f(x)=e^x , g(x)=\ln x$are inverse to each other. There is an infinity of such functions.

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