Question

If f(x) = 3 – 2x and g (x) = StartFraction 1 Over x + 5 EndFraction, what is the value of (StartFraction f Over g EndFraction) (8)?

Answer 1

The value of $(\frac{f}{g})(8)$ is -169

Therefore $(\frac{f}{g})(8)=-169$

Step-by-step explanation:

• Given that the functions f is defined by $f(x)=3-2x$

and g is defined by $g(x)=\frac{1}{x+5}$

To find the $(\frac{f}{g})(8)$

First find $(\frac{f}{g})(x)$

$(\frac{f}{g})(x)=\frac{3-2x}{\frac{1}{x+5}}$

$=\frac{(3-2x)(x+5)}{1}$

$=(3-2x)(x+5)$

$=3(x)+3(5)-2x(x)-2x(5)$

$=3x+15-2x^2-10x$

• Adding the like terms

$=-2x^2-7x+15$

Therefore $(\frac{f}{g})(x)=-2x^2-7x+15$

• Now find $(\frac{f}{g})(8)$
• That is put x=8 in the function $(\frac{f}{g})(x)=-2x^2-7x+15$ we have

$(\frac{f}{g})(8)=-2(8)^2-7(8)+15$

$=-2(64)-56+15$

$=-128-56+15$

$=-169$

Therefore $(\frac{f}{g})(8)=-169$

The value of $(\frac{f}{g})(8)$ is -169