The following function is one-to-one. Find its inverse. Find the domain and range of f and f^-1 f(x) = 2x + 4

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The following function is one-to-one. Find its inverse. Find the domain and range of f and f^-1 f(x) = 2x + 4

Mathematics
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|dw:1328466575161:dw| just switch the x and y and solve for y to get the inverse function
Now for domains:
For the domain of f(x) you just have to look at the equation and ask yourself, " is there any number x could not be?" For example, if that was a sqrt(x) instead of a regular x, there would be limitations (x cannot be negative, b/c you can't take the square root of a negative number).

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So in our example, there's not really anything that could limit x. It could be a positive number, it could be a negative number, it could be a fraction - it could be anything and it would be okay, you could do that computation with no problems. For the range of f(x) now:
You know that y = 2x+4 is a straight line. (if you don't, just graph it on your graphic calculator or even look it up online). A straight line continues in both positive y directions (up) and negative y directions (down) forever. It'll never stop. So, there are no limits on what y can be. So, in conclusion for f(x) the domain is all real numbers, and similarly the range is all real numbers.
Same thing for f(x)^-1, too. Just logically look at the equation and think about limitations. In this case, there are none.

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