Question

For the real-valued functions g(x)=(x-4)/(x+3) and h(x)=2x-1, find the composition of g open circle h and specify its domain using interval notation.

Answer 1

please help me!

Answer 2

Well, do it. Let's see your best algebra.

Answer 3

Im not sure what to do.

Answer 4

Hint: If f(x) = 2x + 1
And r(x) = 3x - 2
f o r(x) = f(r(x)) = 2x + 1 = 2(r(x)) + 1 = 2(3x-2) + 1 = 6x - 4 + 1 = 6x - 3

We are creating new functions by substituting old ones into other old ones.

Answer 5

I still dont understand. Could you show me step by step how to solve it.

Answer 6

Just did. Your turn.

If \(g(x) = \dfrac{x-4}{x+3}\), what is \(g(5)\)?

Answer 7

would that answer to the question be 2x−5/2(x+1)

Answer 8

You didn't answer my question. What is \(g(5)\)?

Answer 9

is it the same as saying g(h(x))? just wanted to know before i asnwer

Answer 10

That's the next question. First, I want to see if you understand the concept of substitution into a function definition.

You can answer wither question. \(g(h(x))\;or\;g(5)\).

Answer 11

\(g(5) = \dfrac{5-4}{5+3}\)

\(g(h(x)) = \dfrac{h(x)-4}{h(x)+3}\)

That's ALL I'm looking for.

Now, substitute in that last statement the definition for h(x) and do some simplifying.