Answer:
1) [tex]h(x) = \frac{f(x)}{g(x)}[/tex], 2) [tex]h(x) = \frac{g(x)}{f(x)}[/tex], 3) [tex]h(x) = f(x) + g(x)[/tex], 4) [tex]h (x) = f [g (x)][/tex], 5) [tex]h(x) = f(x) - g(x)[/tex]
Step-by-step explanation:
1) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h (x) = \frac{x+4}{2\cdot x + 1}[/tex], then:
[tex]h(x) = \frac{f(x)}{g(x)}[/tex]
2) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = \frac{2\cdot x + 1}{x+4}[/tex], then:
[tex]h(x) = \frac{g(x)}{f(x)}[/tex]
3) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = 3\cdot x + 5[/tex], then:
[tex]h(x) = 3\cdot x + 5[/tex]
[tex]h (x) = (1 + 2)\cdot x + (4+1)[/tex]
[tex]h(x) = x + 2\cdot x + 4 +1[/tex]
[tex]h(x) = (x+4) + (2\cdot x + 1)[/tex]
[tex]h(x) = f(x) + g(x)[/tex]
4) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = 2\cdot x + 5[/tex], then:
[tex]h(x) = 2\cdot x + 5[/tex]
[tex]h(x) = 2\cdot x + 1 + 4[/tex]
[tex]h(x) = (2\cdot x +1)+4[/tex]
[tex]h (x) = f [g (x)][/tex]
5) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = -x + 3[/tex], then:
[tex]h(x) = -x + 3[/tex]
[tex]h(x) = (1 - 2)\cdot x + 4 - 1[/tex]
[tex]h(x) = x - 2\cdot x + 4 - 1[/tex]
[tex]h(x) = x + 4 - (2\cdot x + 1)[/tex]
[tex]h(x) = f(x) - g(x)[/tex]
