For \( f(x)=9 x-2 \) and \( g(x)=\frac{x+2}{9} \), find the following functions. a. \( (f \circ g)(x) \); b. \( (g \circ f)(x) \); c. \( (f \circ g)(5) \); d. \( (g \circ f)(5) \) a. \( (f \circ g)(x)=\square \) (Simplify your answer.)

To find \( (f \circ g)(x) \), we will substitute \( g(x) \) into \( f(x) \). 1. We know \( g(x) = \frac{x+2}{9} \). 2. Substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f\left(\frac{x+2}{9}\right) = 9\left(\frac{x+2}{9}\right) - 2 \] 3. Simplifying this, we have: \[ = (x + 2) - 2 = x \] Thus, \( (f \circ g)(x) = x \). Next, let’s find \( (g \circ f)(x) \): 1. We know \( f(x) = 9x - 2 \). 2. Substitute \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(9x - 2) = \frac{(9x - 2) + 2}{9} \] 3. Simplifying this gives: \[ = \frac{9x}{9} = x \] Thus, \( (g \circ f)(x) = x \). Now for \( (f \circ g)(5) \): \[ (f \circ g)(5) = 5 \] And for \( (g \circ f)(5) \): \[ (g \circ f)(5) = 5 \] So, the final answers are: a. \( (f \circ g)(x) = x \) b. \( (g \circ f)(x) = x \) c. \( (f \circ g)(5) = 5 \) d. \( (g \circ f)(5) = 5 \)