Please help me! Have a MATH test tomorrow.?

Question

f(x) = -x^2 + 9
g(x) = 2x^2 + 5x - 3
a) (g-f)(x) pretty sure the answer would be 3x^2 + 5x-12
b) f(g(x)) not really sure on if you would do the negative first or square it first and then take the negative
c) (f/g)(x) pretty sure the answer would be (-x+3)/ (2x-1)

Answer 1

Your answer for (a) is correct.

(b) You would square first, then multiply the result by -1 (and then of course add the 9). If it were intended that the negative be done first, it would be written

f(x) = (-x)² + 9

Your answer for (c) is correct. For completeness, you would need to specify that x cannot be -3 or 1/2 (since g(x) = 0 at those x-values).

Very good! Good luck on the test!