Let f(x) = 2x2 + 5x - 3, 9 (x) = x2 - 4x + 2,
and h (x) = -x? + 4x - 2. Select all of the expressions that
are equivalent to 3x2 + x - 1.
(3 points)
O f(x) + h(x)
O h(x) - f(x)
O g(x) + f(x)
O f(x) - h(x)
O g(x) - h(x)
O f(x) + g(x)
To find which expressions are equivalent to 3x^2 + x - 1, we can substitute the given functions into the expression and simplify.
f(x) = 2x^2 + 5x - 3
h(x) = -x^2 + 4x - 2
f(x) + h(x) = (2x^2 + 5x - 3) + (-x^2 + 4x - 2) = x^2 + 9x - 5
h(x) - f(x) = (-x^2 + 4x - 2) - (2x^2 + 5x - 3) = -3x^2 - x + 1
g(x) = x^2 - 4x + 2
g(x) + f(x) = (x^2 - 4x + 2) + (2x^2 + 5x - 3) = 3x^2 + x - 1
f(x) - h(x) = (2x^2 + 5x - 3) - (-x^2 + 4x - 2) = 3x^2 + x - 1
g(x) - h(x) = (x^2 - 4x + 2) - (-x^2 + 4x - 2) = 2x^2 - 8x + 4
f(x) + g(x) = (2x^2 + 5x - 3) + (x^2 - 4x + 2) = 3x^2 + x - 1
Therefore, the expressions that are equivalent to 3x^2 + x - 1 are:
- f(x) - h(x)
- f(x) + g(x)