which of these functions are the same

Question

which of these functions are the same? $$f(x)=(5^{-x})+3 \, ; g(x)=5^{(3-x)} \, ; h(x)=-5^{(x-3)}$$ i have already tried a lot of things but none of them shows the same function Thank you.

Answer 1

Check each function's value at $0$.

EDIT: Two functions $u$ and $v$ are said to be equal if and only if $u(x)=v(x)$ for all $x$. In particular, if there exists some $x$ so that $u(x)\neq v(x)$, the two functions are not equal.

Answer 2

Nothing wrong with swinging a hammer:

$f(0) = 5^{-0} + 3 = 4$. $g(0) = 5^{3-0} = 125$. $h(0) = -5^{0-3}= -\frac 1{125}$.

Last time I checked, $f(0)= 4 \ne 125=g(0)$. And $f(0)=4 \ne -\frac 1{125}=h(0)$. $g(0) = 125 \ne -\frac 1{125}=h(0)$. .... At least that was the case, last time I checked.

No two of those values are equal so no two of the functions are equal.

It's that simple.