Question

suppose that the functions \\(s\\) and \\(t\\) are defined for all real numbers \\(x\\) as follows.
\\s(x) = 4x^2\\
\\t(x) = x + 5\\
find the following.
\\(t + s)(x) = \\
\\(t \cdot s)(x) = \\
\\(t - s)(-3) = \\

Explanation:

Compute the sum function

$$ (t+s)(x) = t(x) + s(x) = (x+5) + 4x^2 = 4x^2 + x + 5 $$

Compute the product function

$$ (t \cdot s)(x) = t(x) \cdot s(x) = (x+5)(4x^2) = 4x^3 + 20x^2 $$

Compute the difference at the given value

$$
LATEXBLOCK0
$$

Answer:

Suppose that the functions \(s\) and \(t\) are defined for all real numbers \(x\) as follows.

$$
LATEXBLOCK0
$$

Find the following.
\((t+s)(x) =\) <blank>\(4x^2+x+5\)</blank>
\((t \cdot s)(x) =\) <blank>\(4x^3+20x^2\)</blank>
\((t-s)(-3) =\) <blank>\(-34\)</blank>