Functions and Domains

[saj93]

Hi guys, I need help with this problem:



Q.) Find the domain of the function f(x)= [2*sqrt(x-4)]^(x-7)

I got as far as to recognize that the function of the denominator would be undefined at x=7 but when it came to solving the square root on the top,I got a little confused. I know that negative numbers and zero cannot be square-roted so my question is if I put the domain of the equation on top as x>4 am I still right? I'd really appreciate any help guys!! And if possible can you please explain to me why or why not I am wrong/right(so i know how to do it next time)?

Thanks a bunch

 

[pka]

Hi guys, I need help with this problem:
Q.) Find the domain of the function f(x)= [2*sqrt(x-4)]^(x-7)
I got as far as to recognize that the function of the denominator would be undefined at x=7 but when it came to solving the square root on the top,I got a little confused. I know that negative numbers and zero cannot be square-roted so my question is if I put the domain of the equation on top as x>4 am I still right? I'd really appreciate any help guys!! And if possible can you please explain to me why or why not I am wrong/right(so i know how to do it next time)?

You posted \(\displaystyle \displaystyle\left[2\sqrt{x-4}\right]^{x-7}\).

But you write as if you mean \(\displaystyle \dfrac{\sqrt{x-4}}{x-7}\)

Which is it?

 

[mmm4444bot]

zero cannot be square-roted

Yes it can be, actually. The square root of zero is zero.

so my question is if I put the domain of the [expression] on top as x>4 am I still right?

Not if 7 leads to division by zero. (Also, 4 needs to be included.)