Question

If f and g are inverse functions and if (8,3) is a point on the graph of y = g(x) then f is
a. f(x) = x^2-1 b. f(x) = 2x -1 c. f(x) = 〖2x〗^2-1. d. f(x) = 4x

Answer 1

If f and g are inverse functions, then f(g(x)) = x and g(f(x)) = x for all values of x in their respective domains.

Since (8,3) is a point on the graph of y = g(x), we can infer that g(8) = 3.

Using the property of inverse functions, we have f(3) = 8.

Now let's analyze each option:

a. f(x) = x^2 - 1
If we substitute 3 into this equation, we get f(3) = 3^2 - 1 = 9 - 1 = 8. This matches our earlier result, so option A could be a possible answer.

b. f(x) = 2x - 1
Substituting 3 into this equation, we get f(3) = 2(3) - 1 = 6 - 1 = 5. This does not match our earlier result, so option B is not the correct answer.

c. f(x) = 2x^2 - 1
Substituting 3 into this equation, we get f(3) = 2(3)^2 - 1 = 2(9) - 1 = 18 - 1 = 17. This does not match our earlier result, so option C is not the correct answer.

d. f(x) = 4x
Substituting 3 into this equation, we get f(3) = 4(3) = 12. This does not match our earlier result, so option D is not the correct answer.

Based on our analysis, option A (f(x) = x^2 - 1) is the most likely correct answer.