Question

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x)=3x+5 and g(x)=x^2 .
Find g(x)-f(x)

A.) 3x^2-5
B.) x^3-5
C.) 3x^3-5x^2
D.) x^2-3x-5

Please an explanation too:) Thank you!

Answer 1

x² - 3x - 5 ⇒ answer D

Explanation:

* Lets explain how to solve the problem

- There are two functions f(x) ang g(x)

- f(x) = 3x + 5 ⇒ it is a linear function

- g(x) = x² ⇒ it is a quadratic function

- Both functions have a domain the set of real numbers

- We want to subtract f(x) from g(x)

* Lets solve the problem

∵ g(x) = x²

∵ f(x) = 3x + 5

∵ f(x) will subtracted from g(x)

∴ g(x) - f(x) = (g - f)(x)

- Lets make the subtraction

∴ (g - f)(x) = x² - (3x + 5)

- Open the bracket by multiply the negative sign by the two terms

of the bracket

∵ -(3x) = - 3x

∵ -(5) = - 5

∴ (g - f)(x) = x² - 3x - 5

∴ g(x) - f(x) = x² - 3x - 5

Answer 2

D.) x^2-3x-5

Explanation:

f(x)=3x+5

g(x)=x^2 .

Find g(x)-f(x)

g(x) - f(x)= x^2 -(3x+5)

Distribute the minus sign

x^2 -3x-5