g(x)=x^2 - 4 what is g(3x)

Question

g(x)=x^2 - 4 what is g(3x)

Answer 1

If the question were "What is g(2)?", how would you answer?

Just plug in "2" for "x", right?

g(2) = (2)² - 4 = 0

If the question were "What is g(7)?", you would plug in "7" for "x":

g(7) = (7)² - 4 = 45

So, g(3x) means plug in "3x" for "x" making it:

g(3x) = (3x)² - 4 = 9x² - 4

Answer 2

g(x) = x^2 -4

g(3x) = 9x^2 -4

Answer 3

You got this! This is a very straightforward question Michael! Follow this secret recipe to reach the answer in the easiest possible way.

If you were given this same function which is g(x)=x^2-4 and asked what is g(2), you would of simply plugged in the value 2 in the given function.

This would yield: g(2)=2^2-4=0

Think of it in the same exact manner but instead of plugging in the value "2", plug in "3x" in the given equation.

This would yield: g(3x)=(3x)^2-4=9x^2-4.

Very simple, Very straightforward. I offer my online tutoring sessions for $20/hr. If you need further help, feel free to reach out!

Answer 4

Composition of functions works very similar to substitution.

Let's assume we were substituting g(x) with x=1. Then the problem might look like this:

g(x) = x²-4; evaluate at g(1).

g(1) = (1)²-4

= 1 -4

= -3; so g(1) = -3

Now lets evaluate g(x) at 3x. So it follows suit:

g(x) = x²-4; evaluate g(3x)

g(3x) = (3x)²-4

= (3)²(x)² -4

= 9x²-4; so g(3x) = 9x²-4

Answer 5

you can think of "x" as the "input" for the function. The input can be a real number or an expression, such as 3x.

Simply plug 3x into your function:

g(3x) = (3x)² - 4

= 9x² - 4

Answer 6

g(3x) = (3x)² - 4 = 9x² - 4