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2 years ago

Find (f/g) (x) and state the domain restriction. f (x) = 6x - 3 and g(x) = 12x^2 - 6x

Mathematics

1 answer:

Rufina [12.5K]2 years ago

8 0

9514 1404 393

Answer:

(f/g)(x) = 1/(2x)

x ≠ 1/2

Step-by-step explanation:

$(f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{6x-3}{12x^2-6x}=\dfrac{6x-3}{2x(6x-3)}\\\\\boxed{(f/g)(x)=\dfrac{1}{2x}}\quad x\ne\dfrac{1}{2}$

The domain restriction x ≠ 1/2 comes from the requirement to prevent the denominator factor 6x-3 from being zero.

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Which transformations are needed to change the parent cosine function to y = 3 cosine (10 (x minus pi))?

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Answer:

See Explanation

Step-by-step explanation:

Given

New function: $y = 3 \cos(10 (x -\pi))$

We can assume the parent function to be:

$y = \cos (x)$

The new function can be represented as:

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Where

A = Vertical stretch factor

B = Period

C = Right shift

By comparison:

$y = A*\cos((\frac{2\pi}{B})(x-c))$ to $y = 3 \cos(10 (x -\pi))$

$A = 3$

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Solve for B

$B = \frac{2\pi}{10}$

$B = \frac{\pi}{5}$

Using the calculated values of $A,\ B\ and\ c.$ This implies that, the following transformations occur on the parent function:

Vertically stretched by $3$
Horizontally compressed by $\frac{\pi}{5}$
Right shifted by $\pi$

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