Answer :
Answer:
3
Step-by-step explanation:
[tex](g.f)(x) = g(f(x)) = 2( \frac{1}{2} x - 3) + 5 \\ = x - 6 + 5 = x - 1 \\ then \\ (g.f)(4) = 4 - 1 = 3[/tex]
Functions can be combined to create another.
The value of [tex]\mathbf{(g\cdot f)(4) }[/tex] is -13.
The functions are given as:
[tex]\mathbf{f(x) = \frac 12x - 3}[/tex]
[tex]\mathbf{g(x) = 2x + 5}[/tex]
[tex]\mathbf{(g\cdot f)(x)}[/tex] is calculated as:
[tex]\mathbf{(g\cdot f)(x) = g(x) \times f(x)}[/tex]
So, we have:
[tex]\mathbf{(g\cdot f)(x) = (2x + 5) \times (\frac 12x - 3)}[/tex]
Substitute 4 for x
[tex]\mathbf{(g\cdot f)(4) = (2(4) + 5) \times (\frac 12(4) - 3)}[/tex]
[tex]\mathbf{(g\cdot f)(4) = (8 + 5) \times (2 - 3)}[/tex]
[tex]\mathbf{(g\cdot f)(4) = (13) \times (- 1)}[/tex]
[tex]\mathbf{(g\cdot f)(4) = -13}[/tex]
Hence, the value of [tex]\mathbf{(g\cdot f)(4) }[/tex] is -13.
Read more about composite functions at:
https://brainly.com/question/20379727