Question

If f(x) = 5x2 – 6x + 13 and g(x) = 6 – 4(x – 1) which is an equivalent form of f(x) + g(x)?

Answer 1

To find an equivalent form of f(x) + g(x), we simplify g(x) by distributing -4 and then add the expressions together. The final result is 5x^2 - 10x + 23 after combining like terms.

Step-by-step explanation:

To find an equivalent form of f(x) + g(x), where f(x) = 5x2 − 6x + 13 and g(x) = 6 − 4(x − 1), we first need to simplify g(x). When we distribute the -4 across the parenthesis inside g(x), we get g(x) = 6 − 4x + 4. Now, g(x) is simplified to g(x) = 10 − 4x. Adding f(x) and g(x) gives us:

• f(x) = 5x2 − 6x + 13
• g(x) = 10 − 4x

So,

• f(x) + g(x) = (5x2 − 6x + 13) + (10 − 4x)

Combining like terms, we get:

f(x) + g(x) = 5x2 − 10x + 23