W Write an equation of A-line that passes through the point (2,0) and is perpendicular to the line y= -1/2x + 3

1 answer:

8 0

Perpendicular is opposite sign and reciprocal
-1/2 = 2, the slope is 2
Y = 2x + b, plug in point
0 = 4 + b, b = -4
Equation: y = 2x - 4

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For f(x) = 4x +1 and g(x) = x2 - 5, find (g/f) (x).

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Answer:

$\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

Step-by-step explanation:

$f(x)=4x+1$

$g\left(x\right)=x^2\:-\:5$

(g/f)(x) = g(x) / f(x)

$=\:\frac{x^2\:-\:5}{4x+1}\:\:\:\:\:\:$

$=\frac{x}{4}+\frac{-\frac{x}{4}-5}{4x+1}$

$=\frac{x}{4}-\frac{1}{16}+\frac{-\frac{79}{16}}{4x+1}$

$=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

Therefore,

$\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

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