Question

Find the difference: f ( x ) − g ( x ) when f ( x ) = 4 x 5 + 10 x 2 − 6 x and g ( x ) = − 2 x 5 + 8 x 2 − 4 .

Answer 1

6x^5 + 2x^2 - 6x + 4

Explanation:

To find the difference between two functions, f(x) - g(x), you simply subtract the second function (g(x)) from the first function (f(x)).

f(x) = 4x^5 + 10x^2 - 6x

g(x) = -2x^5 + 8x^2 - 4

Now, subtract g(x) from f(x):

f(x) - g(x) = (4x^5 + 10x^2 - 6x) - (-2x^5 + 8x^2 - 4)

Now, let's simplify this expression:

f(x) - g(x) = 4x^5 + 10x^2 - 6x + 2x^5 - 8x^2 + 4

Combine like terms:

f(x) - g(x) = (4x^5 + 2x^5) + (10x^2 - 8x^2) - 6x + 4

f(x) - g(x) = 6x^5 + 2x^2 - 6x + 4

So, the difference between f(x) and g(x) is:

6x^5 + 2x^2 - 6x + 4