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Which of the following is not true about the inverse of f(x) = -3x+5?

A. The domain of f-1(2) is (-0,00)
B. f-1(x) has a constant rate of change
C. The x-intercept of f++(x) is (,0)
D. The range of f-1(x) is (-00,00)

1 Answer

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Final answer:

The inverse of the function f(x) = -3x+5 can be found by switching the x and y variables and solving for y. For each statement, option A is not true because the domain of f-1(2) is a single point, not an interval. Option B is true because the inverse function has a constant rate of change. Option C is not true because the x-intercept of f(x) is (5/3, 0), not (0, 0). Option D is true because the range of the inverse function is (-∞,∞).

Step-by-step explanation:

The inverse of the function f(x) = -3x+5 can be found by switching the x and y variables and solving for y. So, let's start:

  1. Swap the x and y: x = -3y+5
  2. Solve for y: -3y = x-5
  3. Divide by -3 on both sides: y = (x-5)/-3 = 5/3 - x/3

Now, let's address each statement:

A. The domain of f-1(2) is (-∞,0): Since the inverse function finds the y-values for a given x-value, the statement is not true. The domain of f-1(2) is the set of x-values that make the expression (x-5)/-3 = 2 true, which is a single point, not an interval.

B. f-1(x) has a constant rate of change: This statement is true. The inverse function f-1(x) is a straight line with a constant rate of change because its equation is linear.

C. The x-intercept of f(x) is (0,0): Since the original function f(x) = -3x+5 is a straight line, its x-intercept is the point where y is equal to 0. By substituting y = 0 in the equation and solving for x, we find that the x-intercept is (5/3, 0), not (0, 0).

D. The range of f-1(x) is (-∞,∞): Since the inverse function f-1(x) is a straight line with a slope of -1/3, its range is (-∞,∞), meaning it takes on all possible y-values.

User Thomas Strub
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