Mathematics: Find each of the following values given that f(x)equals startfraction 1 over startroot x plus 5 endroot endfraction and g(x)equals 3x plus 1. a. (fplusg)(negative 4) b. (fminusg)(0) c. (ftimesg)(negative 1) d. (startfraction f over g endfraction )(1)

You just have to rearrange the formula.So:765 = 135 x m + 225765 - 225 = 135 x m540 = 135 x mm = 540 / 135m = 4So four months....

Find each of the following values given that f(x)equals

Ответ:

joelpimentel

06.01.2022

Mathematics

a. (f+g)(-4)=-10

b. $(f-g)(0)=\frac{1}{\sqrt{5} } -1$

c. (fg)(-1)=-1

d. $(\frac{f}{g})(1)=\frac{1}{4\sqrt{6} }$

Step-by-step explanation:

Given that:

$f(x)=\frac{1}{\sqrt{x+5} }$

g(x)=3x+1

The sum, rest, multiplication or division of functions are calculated as following:

$(f+g)(x)=f(x)+g(x)\\(f-g)(x)=f(x)-g(x)\\(fg)(x)=f(x)g(x)\\(\frac{f}{g} )(x)=\frac{f(x)}{g(x)}$

For values of x where f(x) and g(x) are defined and in the case of $(\frac{f}{g} )(x)$ for values of g(x) different from zero.

Taking into account that f(x) and g(x) are defined for values of x equals to -4, 0, 1 and -1 and g(1) is different from zero, we get:

$(f+g)(x)=f(x)+g(x)\\(f+g)(x)=\frac{1}{\sqrt{x+5} } +3x+1\\(f+g)(-1)=\frac{1}{\sqrt{-4+5} } +3(-4)+1\\(f+g)(-1)=-10$

$(f-g)(x)=f(x)-g(x)\\(f-g)(x)=\frac{1}{\sqrt{x+5} } -(3x+1)\\(f-g)(0)=\frac{1}{\sqrt{0+5} } -(3(0)+1)\\(f-g)(0)=\frac{1}{\sqrt{5} } -1$

$(fg)(x)=f(x)g(x)\\(fg)(x)=\frac{1}{\sqrt{x+5} } (3x+1)\\(fg)(-1)=(\frac{1}{\sqrt{-1+5} } )(3(-1)+1)\\(fg)(-1)=-1$

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)} \\(\frac{f}{g})(x)=\frac{1}{(\sqrt{x+5})(3x+1)} \\(\frac{f}{g})(1)=\frac{1}{(\sqrt{1+5})(3(1)+1)}\\(\frac{f}{g})(1)=\frac{1}{4\sqrt{6} }$

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Find each of the following values given that f(x)equals startfraction 1 over startroot x plus 5 endroot endfraction and g(x)equals 3x plus 1. a. (fplusg)(negative 4) b. (fminusg)(0) c. (ftimesg)(negative 1) d. (startfraction f over g endfraction )(1)

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