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Oksanka [162]
3 years ago
8

Using ƒ(x) = 3x − 3 and g(x) = -x, find g(ƒ(x)) a. 3x+3 b. 3-3x c.-3-3x d. 2x-3

Mathematics
1 answer:
Tresset [83]3 years ago
8 0
<h3>Answer:  Choice B.  3 - 3x</h3>

Work Shown:

g(x) = -x\\\\g(f(x)) = -f(x)\\\\g(f(x)) = -(3x-3)\\\\g(f(x)) = -3x+3\\\\g(f(x)) = \boldsymbol{3-3x}\\\\

Explanation: We start with the outer function g(x). In the second step, we replace every copy of x with f(x). From there we plug in f(x) = 3x-3 and simplify using the distribution rule.

The notation g(f(x)) is the same as writing (g \circ f)(x)

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40 quizzes

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sineoko [7]

Answer:

(g+f)(x)=(2^x+x-3)^(1/2)

Step-by-step explanation:

Given  

f(x)= 2^(x/2)

And

g(x)= √(x-3)

We have to find (g+f)(x)

In order to find (g+f)(x), both the functions are added and simplified.

So,

(g+f)(x)= √(x-3)+2^(x/2)  

The power x/2 can be written as a product of x*(1/2)

(g+f)(x)= √(x-3)+(2)^(1/2*x)

We also know that square root dissolves into power ½

(g+f)(x)=(x-3)^(1/2)+(2)^(1/2*x)

We can see that power ½ is common in both functions so taking it out

(g+f)(x)=(x-3+2^x)^(1/2)

Arranging the terms

(g+f)(x)=(2^x+x-3)^(1/2)  ..

5 0
3 years ago
The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a n
xz_007 [3.2K]

Answer:

(15,595, 16,805)

Step-by-step explanation:

We have to:

m = 16.2, sd = 3.75, n = 150

m is the mean, sd is the standard deviation and n is the sample size.

the degree of freedom would be:

n - 1 = 150 - 1 = 149

df = 149

at 95% confidence level the t is:

alpha = 1 - 95% = 1 - 0.95 = 0.05

alpha / 2 = 0.05 / 2 = 0.025

now well for t alpha / 2 (0.025) and df (149) = t = 1,976

the margin of error = E = t * sd / (n ^ (1/2))

replacing:

E = 1,976 * 3.75 / (150 ^ (1/2))

E = 0.605

The 95% confidence interval estimate of the popilation mean is:

m - E <u <m + E

16.2 - 0.605 <u <16.2 + 0.605

15,595 <u <16,805

(15,595, 16,805)

5 0
3 years ago
*10 POINTS * <br> find the value of x <br><br> x = ___??
Paladinen [302]
The value is 22 because I took the test
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3 years ago
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PLZ HELP SCALE FACTOR TRIANGLE<br><br> A. 10.5 cm<br> B. 31.5 cm<br> C. 63 cm<br> D. 189 cm
Anarel [89]

If two similar triangles have sides in the ratio a : b, then their areas are in the ratio a² : b².

We have the ratio:

54:18=\dfrac{54}{18}=3:1

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Area of the larger triangle = 567 cm²

Therefore we have the equation:

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<h3>Answer: C. 63 cm²</h3>
3 0
2 years ago
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