Question

For questions 8 – 14, use the following functions:

Answer 1

we are given

$f(x)=5$

$g(x)=\sqrt{x+2}$

(8)

$(f+g)(x)=f(x)+g(x)$

we can plug it

$(f+g)(x)=5+\sqrt{x+2}$

(9)

$(f-g)(x)=f(x)-g(x)$

we can plug it

$(f-g)(x)=5-\sqrt{x+2}$

(10)

$(f*g)(x)=f(x)*g(x)$

we can plug it

$(f*g)(x)=5\sqrt{x+2}$

(11)

$(\frac{f}{g} )(x)=\frac{f(x)}{g(x)}$

we can plug it

$(\frac{f}{g} )(x)=\frac{5}{\sqrt{x+2}}$

(12)

$(\frac{g}{f} )(x)=\frac{g(x)}{f(x)}$

we can plug it

$(\frac{g}{f} )(x)=\frac{\sqrt{x+2}}{5}$

(13)

$(fog)(x)=f(g(x))$

$f(x)=5$

we can replace g(x)

we get

$(fog)(x)=5$

(14)

$(gof)(x)=g(f(x))$

$f(x)=5$

we can replace f(x)

$(gof)(x)=\sqrt{f(x)+2}$

we get

$(gof)(x)=\sqrt{5+2}$

$(gof)(x)=\sqrt{7}$