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For questions 8 – 14, use the following functions:

f(x)=5

g(x)=sqrt x+2


8. Find (f+g(x).

9. Find (f-g)(x).

10. Find (f*g)(x).

11. Find (f/g)(x).
12. Find (g/f)(x).

13. Find (fog)(x)
14. Find (gof)(x)

Respuesta :

we are given

[tex]f(x)=5[/tex]

[tex]g(x)=\sqrt{x+2}[/tex]

(8)

[tex](f+g)(x)=f(x)+g(x)[/tex]

we can plug it

[tex](f+g)(x)=5+\sqrt{x+2}[/tex]

(9)

[tex](f-g)(x)=f(x)-g(x)[/tex]

we can plug it

[tex](f-g)(x)=5-\sqrt{x+2}[/tex]

(10)

[tex](f*g)(x)=f(x)*g(x)[/tex]

we can plug it

[tex](f*g)(x)=5\sqrt{x+2}[/tex]

(11)

[tex](\frac{f}{g} )(x)=\frac{f(x)}{g(x)}[/tex]

we can plug it

[tex](\frac{f}{g} )(x)=\frac{5}{\sqrt{x+2}}[/tex]

(12)

[tex](\frac{g}{f} )(x)=\frac{g(x)}{f(x)}[/tex]

we can plug it

[tex](\frac{g}{f} )(x)=\frac{\sqrt{x+2}}{5}[/tex]

(13)

[tex](fog)(x)=f(g(x))[/tex]

[tex]f(x)=5[/tex]

we can replace g(x)

we get

[tex](fog)(x)=5[/tex]

(14)

[tex](gof)(x)=g(f(x))[/tex]

[tex]f(x)=5[/tex]

we can replace f(x)

[tex](gof)(x)=\sqrt{f(x)+2}[/tex]

we get

[tex](gof)(x)=\sqrt{5+2}[/tex]

[tex](gof)(x)=\sqrt{7}[/tex]


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