. If f(x)=5x-25 and g(x)=(1)/(5)x+5 which expression could be used to verify g(x) is the inverse of f(x) i (1)/(5)((1)/(5)x+5)+5 (1)/(5)(5x-25)+5 (1)/((frac (1)(5)x+5)) 5((1)/(5)x+5)+5

To verify that $g(x)$ is the inverse of $f(x)$, we need to show that $f(g(x)) = x$ and $g(f(x)) = x$.<br /><br />Let's start by finding $f(g(x))$:<br /><br />$f(g(x)) = f\left(\frac{1}{5}x + 5\right) = 5\left(\frac{1}{5}x + 5\right) - 25 = x + 25 - 25 = x$<br /><br />Now, let's find $g(f(x))$:<br /><br />$g(f(x)) = g(5x - 25) = \frac{1}{5}(5x - 25) + 5 = x - 5 + 5 = x$<br /><br />Since both $f(g(x)) = x$ and $g(f(x)) = x$, we can conclude that $g(x)$ is the inverse of $f(x)$.<br /><br />Therefore, the correct expression to verify that $g(x)$ is the inverse of $f(x)$ is $\frac{1}{5}(5x - 25) + 5$.