contestada

Given: g(x)=1/x+2 and h(x)=3x Check all restrictions on the domain of gOh.
1. x does not equal 0
2. x does not equal -2
3. x does not equal -2/3
4. there are no restrictions

Respuesta :

The composite function [tex] (g \circle h)(x) [/tex] works like this:

  • Take a number [tex] x [/tex] as input
  • Evaluate h(x) = 3x. Let's call this output z.
  • Evaluate g(x) = 1/(z+2)

So, if we substitute back z = 3x, the final output is 1/(3x+2). We know that the denominator of a fraction can't be zero, so we must impose

[tex] 3x+2 \neq 0 \iff 3x \neq -2 \iff x \neq -\dfrac{2}{3} [/tex]

x not equal to -2/3 is the answer.

Otras preguntas