Suppose that $f(x)=5 x-1$ and $g(x)=-4 x+8$. (a) Solve $f(x)=0$. (b) Solve $f(x)>0$. (c) Solve $f(x)=g(x)$. (d) Solve $f(x) \leq g(x)$. (e) Graph $y=f(x)$ and $y=g(x)$ and find the point that represents the solution to the equation $f(x)=g(x)$. (a) For what value of $x$ does $f(x)=0$ ? \[ x=\frac{1}{5} \] (Type an integer or a simplified fraction.) (b) For which values of $x$ is $f(x)>0$ ? (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Step 1 ：First, we need to solve for $x$ when $f(x) = 0$. This means we need to set the equation $5x - 1 = 0$ and solve for $x$.

Step 2 ：By adding 1 to both sides of the equation, we get $5x = 1$.

Step 3 ：Then, we divide both sides of the equation by 5 to solve for $x$, which gives us $x = \frac{1}{5}$.

Step 4 ：Next, we need to find the values of $x$ for which $f(x) > 0$. This means we need to find the values of $x$ for which $5x - 1$ is greater than 0.

Step 5 ：By adding 1 to both sides of the inequality, we get $5x > 1$.

Step 6 ：Then, we divide both sides of the inequality by 5 to solve for $x$, which gives us $x > \frac{1}{5}$.

Step 7 ：Final Answer: (a) The value of $x$ for which $f(x)=0$ is \(\boxed{\frac{1}{5}}\). (b) The values of $x$ for which $f(x)>0$ are \(\boxed{( \frac{1}{5}, \infty )}\).