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Here are the steps to solve the given problem: The functions are defined as: f(x) = 3x+7 g(x) = (1)/(x) (Assuming the denominator for g(x) is x, as "x00" is not a standard mathematical notation for a function. If it was intended to be x · 100, the problem would be g(x) = (1)/(100x).) a) Find f(2) Step 1: Substitute x=2 into f(x) Substitute x=2 into the function f(x) = 3x+7. f(2) = 3(2) + 7 f(2) = 6 + 7 f(2) = 13 The value of f(2) is 13. b) State the domain of f(x) Step 1: Identify the type of function The function f(x) = 3x+7 is a linear polynomial function. Polynomial functions are defined for all real numbers. The domain of f(x) is R or (-, ). c) Evaluate g(4) Step 1: Substitute x=4 into g(x) Substitute x=4 into the function g(x) = (1)/(x). g(4) = (1)/(4) The value of g(4) is (1)/(4). d) Find gf(x) and its domain Step 1: Find the composite function gf(x) The composite function gf(x) means g(f(x)). We substitute f(x) into g(x). gf(x) = g(f(x)) Since f(x) = 3x+7, we have: gf(x) = g(3x+7) Now, substitute (3x+7) into g(x) = (1)/(x): gf(x) = (1)/(3x+7) The composite function is gf(x) = (1)/(3x+7). Step 2: Determine the domain of gf(x) For gf(x) = (1)/(3x+7) to be defined, the denominator cannot be zero. 3x+7 ≠ 0 3x ≠ -7 x ≠ -(7)/(3) The domain of gf(x) is all real numbers except x = -(7)/(3). The domain of gf(x) is R \-(7)/(3)\ or (-, -(7)/(3)) (-(7)/(3), ). e) Find f^-1(x) Step 1: Set y = f(x) Let y = 3x+7. Step 2: Swap x and y x = 3y+7 Step 3: Solve for y Subtract 7 from both sides: x-7 = 3y Divide by 3: y = (x-7)/(3) So, the inverse function is f^-1(x) = (x-7)/(3). The inverse function is f^-1(x) = (x-7)/(3). What's next?