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 the composite functions \( (f \circ g)(x) \) and \( (g \circ f)(x) \), we need to substitute the function \( g(x) \) into \( f(x) \) and vice versa. a. To find \( (f \circ g)(x) \), we substitute \( g(x) \) into \( f(x) \): \[ (f \circ g)(x) = f(g(x)) = 9 \cdot \frac{x+2}{9} - 2 \] b. To find \( (g \circ f)(x) \), we substitute \( f(x) \) into \( g(x) \): \[ (g \circ f)(x) = g(f(x)) = \frac{9x-2+2}{9} \] c. To find \( (f \circ g)(5) \), we substitute \( x = 5 \) into the expression for \( (f \circ g)(x) \): \[ (f \circ g)(5) = 9 \cdot \frac{5+2}{9} - 2 \] d. To find \( (g \circ f)(5) \), we substitute \( x = 5 \) into the expression for \( (g \circ f)(x) \): \[ (g \circ f)(5) = \frac{9 \cdot 5 - 2 + 2}{9} \] Now, let's simplify these expressions. Simplify the expression by following steps: - step0: Solution: \(\frac{9\left(x+2\right)}{9}-2\) - step1: Reduce the fraction: \(\left(x+2\right)-2\) - step2: Remove the parentheses: \(x+2-2\) - step3: Remove the opposites: \(x\) a. \( (f \circ g)(x) = x \) b. \( (g \circ f)(x) = \frac{9x}{9} = x \) c. \( (f \circ g)(5) = 5 \) d. \( (g \circ f)(5) = 5 \)