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3 years ago

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For the real valued functions f(x) = x-4/x-5 and g(x) = 4x+17, find the composition fog and specify its domain using interval no

tation.
(F o g)(x)=
Domain of f o g:

1 answer:

Studentka2010 [4]3 years ago

3 0

Answer:

(f o g)(x) = $\frac{4x+13}{4x+12}$

Domain : (-∞, -3) ∪ (-3, ∞)

Step-by-step explanation:

Given : f(x) = $\frac{x-4}{x-5}$

g(x) = 4x + 17

We have to find the value of (f o g)(x).

Since (f o g)(x) = f[g(x)]

= $\frac{(4x+17)-4}{(4x+17)-5}$

= $\frac{4x+13}{4x+12}$

For the Domain of the function (f o g)(x),

Given function is defined for (4x + 12) ≠ 0

4x ≠ -12

x ≠ -3

Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)

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How many seconds will light leaving Los Angeles take to reach the following locations (a) San Francisco (about 500km), (b) Londo

kondor19780726 [428]

Answer:

a) It takes 0.0017s for the light to reach San Francisco.

b) It takes 0.033s for the light to reach London.

c) It takes 1.334s for the light to reach Mars.

d) It takes 149.7s for the light to reach Venus.

Step-by-step explanation:

Here we can solve this problem by using this following formula:

$s = \frac{d}{t}$

In which s is the speed(in km/s), d is the distance(in km) and t is the time(in s).

The light speed is 299 792 458 m / s = 299,792.458 km/s, so $s = 299,792.458$

(a) San Francisco (about 500km)

Find t when $d = 500$ . So

$s = \frac{d}{t}$

$299,792.458 = \frac{500}{t}$

$299,792.458t = 500$

$t = \frac{500}{299,792.458}$

$t = 0.0017s$

It takes 0.0017s for the light to reach San Francisco.

b) London(about 10,000km)

Find t when $d = 10,000$ . So

$s = \frac{d}{t}$

$299,792.458 = \frac{10,000}{t}$

$299,792.458t = 10,000$

$t = \frac{10,000}{299,792.458}$

$t = 0.033s$

It takes 0.033s for the light to reach London.

(c) the Moon (400,000km)

Find t when $d = 400,000$ . So

$s = \frac{d}{t}$

$299,792.458 = \frac{400,000}{t}$

$299,792.458t = 400,000$

$t = \frac{400,000}{299,792.458}$

$t = 1.334s$

It takes 1.334s for the light to reach Mars.

(d) Venus (0.3 A.U. from Earth at its closest approach).

Each A.U. has 149,59,7871 km.

So 0.3 A.U. = 0.3*(149,597,871) = 44,879,361.3. This means that $d = 44,879,361.3$ . So:

$s = \frac{d}{t}$

$299,792.458 = \frac{44,879,361.3}{t}$

$299,792.458t = 44,879,361.3$

$t = \frac{44,879,361.3}{299,792.458}$

$t = 149.7s$

It takes 149.7s for the light to reach Venus.

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Answer:

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Stells [14]

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jolli1 [7]

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