Question

The domain for f(x) and g(x) is all real numbers. Let f(x) = x2 + x-20 and g(x) = 3x-12
Find g(x)/f(x)and state its domain.

Answer 1

@AngeI @Shadow

Answer 2

Oh simply just put each equation on either the numerator and denominator given the problem

\(\dfrac{g(x)}{f(x)}-> \dfrac{3x-12}{x^2+x-20}\)

Answer 3

Now we know that the denominator cannot equal 0

So set the denominator equal to 0 to see which values are not within the range

Answer 4

@dude not sure what you mean by setting the denominator equal to 0?

Answer 5

@Vocaloid

Answer 6

\(x^2 + x-20=0\)

Solve for x

Answer 7

@dude x=4, -5?

Answer 8

Other way around sign

-4 and 5

So you domain would be all real number except -4 and 5

Answer 9

@dude what's g(x)/f(x)?

Answer 10

\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
Oh simply just put each equation on either the numerator and denominator given the problem

\(\dfrac{g(x)}{f(x)}-> \dfrac{3x-12}{x^2+x-20}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 11

@mhchen @Vocaloid @dude Mathway says the answer is 3/x+5, but idk how to get there

Answer 12

\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
Oh simply just put each equation on either the numerator and denominator given the problem

\(\dfrac{g(x)}{f(x)} = \dfrac{3x-12}{x^2+x-20}\)
\(\color{#0cbb34}{\text{End of Quote}}\)
\(\color{#0cbb34}{\text{End of Quote}}\)
\[=\frac{3(x-4)}{(x-4)(x+5)}\]

Answer 13

@mhchen thank you so much, I got it now