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aniked [119]
3 years ago
14

What is g^-1(x)? What is the domain of g^-1(x)?

Mathematics
1 answer:
Marina CMI [18]3 years ago
5 0

Answer:

g⁻¹(x) = 1/x - 4

(-∞, 0)∪(0, ∞)

Step-by-step explanation:

To find g⁻¹(x), switch the places of x and y.  Rearrange the equation so that it is equal to y.

g(x) = 1/(x + 4)

x = 1/(y + 4)

x(y + 4) = (1/(y + 4))(y + 4)

x(y + 4) = 1

(x(y + 4))/x = 1/x

y + 4 = 1/x

y + 4 - 4 = 1/x - 4

y = 1/x - 4

g⁻¹(x) = 1/x - 4

For the domain, you need to look at where x is located in the equation.  For this equation, x is in the denominator by itself.  A fraction cannot have a denominator of 0.  This means that x cannot be equal to 0.  The domain is:

(-∞, 0)∪(0, ∞)

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x = 1

Step-by-step explanation:

Subtract 10 from 8 to get -2. Then divide -2x by itself so it will cancel out. Whatever you do to one side of the equation, do to the other so divide -2 by -2 to get your answer of 1

3 0
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Step-by-step explanation:

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what is the equation, in slope- intercept form, of the line that contains the points (-3,4) and (5,7)
gavmur [86]

Answer:

y = \frac{3}{8} x + \frac{41}{8}

Step-by-step explanation:

the equation of a line in slope- intercept form is

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To calculate the slope use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

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m = \frac{7-4}{5+3} = \frac{3}{8}, hence

y = \frac{3}{8} x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

using (5, 7 ), then

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6 0
3 years ago
A boat goes 24 miles at a constant speed in 4 hours against a river current.
Ne4ueva [31]

Answer:

8 miles per hour.

Step-by-step explanation:

24miles in 4 hours = 24/4=6 miles per hour.

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Please help on my hw, I'm not feeling good, and can't concentrate
sergiy2304 [10]

Answer:

Solution given:

f(x)=x²

g(x)=x+5

h(x)=4x-6

now

23:

(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25

24:

(gof)(x)=g(f(x))=g(x²)=x²+5

25:

(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36

26:

(hof)(x)=h(f(x))=h(x²)=4x²-6

27;

(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1

28:

(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14

5 0
3 years ago
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