To solve the equation \( f(x) = 0 \) for the function \( f(x) = \frac{7}{6}x - 7 \), we'll follow the instructions given for parts (a), (b), and (c).
(a) Solve \( f(x) = 0 \)
Setting the function equal to zero:
\[ \frac{7}{6}x - 7 = 0 \]
To solve for \( x \), first add \( 7 \) to both sides:
\[ \frac{7}{6}x = 7 \]
Next, multiply both sides by \( \frac{6}{7} \) to isolate \( x \):
\[ x = 7 \cdot \frac{6}{7} \]
Simplifying gives:
\[ x = 6 \]
So, the solution to \( f(x) = 0 \) is:
\[ \boxed{6} \]
(b) What is the x-intercept?
The x-intercept of a graph occurs where \( y = f(x) = 0 \). Since we found that \( f(x) = 0 \) at \( x = 6 \), the x-intercept is:
\[ (6, 0) \]
The x-intercept is:
\[ \boxed{6} \]
(c) What is the zero of \( f(x) \)?
The zero of a function is the value of \( x \) for which \( f(x) = 0 \). Since we just found that when \( f(x) = 0 \), \( x = 6 \), the zero of \( f(x) \) is:
\[ \boxed{6} \]
In summary:
- \( f(x) = 0 \) solution: \( x = 6 \)
- x-intercept: \( 6 \)
- Zero of \( f(x) \): \( 6 \)