Question

What is the value of the expression (f-h)(x), where f(x) and h(x) are defined as follows?

i) f(x) = -7x^3 + 11x^2 - 8x + 4
ii) h(x) = -x^3 + \frac{3}{5}x^2 - 5x + 2

Answer 1

The value of the expression (f-h)(x), given f(x) and h(x), is -6x^3 + \(\frac{52}{5}x^2 - 3x + 2.

Step-by-step explanation:

To find the value of the expression (f-h)(x), where f(x) and h(x) are defined as:

• f(x) = -7x^3 + 11x^2 - 8x + 4
• h(x) = -x^3 + \(\frac{3}{5}x^2 - 5x + 2\)

We need to subtract h from f. This means subtracting the coefficients of the corresponding powers of x from each other:

1. For x3: -7 - (-1) = -7 + 1 = -6
2. For x2: 11 - \(\frac{3}{5}\) = \(\frac{55}{5} - \frac{3}{5}\) = \(\frac{52}{5}\)
3. For x: -8 - (-5) = -8 + 5 = -3
4. For the constant term: 4 - 2 = 2

Therefore, the resulting function (f-h)(x) is -6x^3 + \(\frac{52}{5}x^2 - 3x + 2.