Question

find the formulas for the functions ( f + g ), ( f - g ), and ( fg ). give the domain of each. ( f(x) = x^2 ) and ( g(x) = 6x - 10 ) ( f + g = square ) (simplify your answer.) the domain of ( f + g ) is ( square ). (type your answer in interval notation.) ( f - g = square ) (simplify your answer.) the domain of ( f - g ) is ( square ). (type your answer in interval notation.) ( fg = square ) (simplify your answer.) the domain of ( fg ) is ( square ). (type your answer in interval notation.)

Explanation:

Step1: Compute $f+g$

$f(x)+g(x) = x^2 + (6x - 10) = x^2 + 6x - 10$

Step2: Find domain of $f+g$

Both $f(x)$ and $g(x)$ are polynomials, defined for all real numbers. Domain: $(-\infty, \infty)$

Step3: Compute $f-g$

$f(x)-g(x) = x^2 - (6x - 10) = x^2 - 6x + 10$

Step4: Find domain of $f-g$

Both $f(x)$ and $g(x)$ are polynomials, defined for all real numbers. Domain: $(-\infty, \infty)$

Step5: Compute $fg$

$f(x) \cdot g(x) = x^2(6x - 10) = 6x^3 - 10x^2$

Step6: Find domain of $fg$

Both $f(x)$ and $g(x)$ are polynomials, defined for all real numbers. Domain: $(-\infty, \infty)$

Answer:

$f+g = x^2 + 6x - 10$
The domain of $f+g$ is $(-\infty, \infty)$

$f-g = x^2 - 6x + 10$
The domain of $f-g$ is $(-\infty, \infty)$

$fg = 6x^3 - 10x^2$
The domain of $fg$ is $(-\infty, \infty)$