Question

Use the given functions to answer the question.f(x) = x² + 2x − 5

g (x) = −3x² − 4x + 1
What is f(x) = g(x)?
a) −2x² + 6x − 6
b) −232 − 2x − 4
c) 422 − 2x − 4
d) 4x² + 6x − 6

Answer 1

To find f(x) = g(x), set the functions equal to each other, solve the resulting quadratic equation using the quadratic formula, and get two possible solutions for x.

Step-by-step explanation:

To find f(x) = g(x), we need to set the two functions equal to each other and solve for x. So, we have:
f(x) = g(x)
x² + 2x - 5 = -3x² - 4x + 1

Combining like terms, we get:
4x² + 6x - 6 = 0

Now, we can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values for a, b, and c, we get:
x = (-6 ± √(6² - 4(4)(-6))) / (2(4))

Simplifying further, we have:
x = (-6 ± √(36 + 96)) / 8
x = (-6 ± √132) / 8

This leads to two possible solutions for x:
x = (-6 + √132) / 8 and x = (-6 - √132) / 8

Therefore, option d) 4x² + 6x - 6 corresponds to f(x) = g(x).