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kiruha [24]
3 years ago
7

Which algebraic expression represents “the difference of 54 and a number”? HELP I AM TIMED ASAP

Mathematics
1 answer:
DedPeter [7]3 years ago
7 0

Answer:

The first one

Step-by-step explanation:

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Step-by-step explanation:

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The distance d, in centimeters, that a diving board bends below its resting position when you stand at its end is dependent on y
kaheart [24]

Answer:

d(1) = -3 and d(2)= -28

Step-by-step explanation:

Given that the distance d, in centimeters, that a diving board bends below its resting position when you stand at its end is dependent on your distance x, in meters, from the stabilized point

d(x)=-4x^3+x^2

For finding out the distances for x=1 and x=2

let us substitute 1 and 2 for x

d(1) = -4(1^3)+1^2 = -3

d(2) = -4(2^3)+2^2 \\= -28

d(1) = -3 and d(2)= -28

3 0
3 years ago
A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u
Kryger [21]

Given: f(x) = \frac{1}{x-2}

           g(x) = \frac{2x+1}{x}

A.)Consider

f(g(x))= f(\frac{2x+1}{x} )

f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}

f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}

f(\frac{2x+1}{x} )=\frac{x}{1}

f(\frac{2x+1}{x} )=1

Also,

g(f(x))= g(\frac{1}{x-2} )

g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}

g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}

g(\frac{1}{x-2} )= \frac{x }{1}

g(\frac{1}{x-2} )= x


Since, f(g(x))=g(f(x))=x

Therefore, both functions are inverses of each other.


B.

For the Composition function f(g(x)) = f(\frac{2x+1}{x} )=x

Since, the function f(g(x)) is not defined for x=0.

Therefore, the domain is (-\infty,0)\cup(0,\infty)


For the Composition function g(f(x)) =g(\frac{1}{x-2} )=x

Since, the function g(f(x)) is not defined for x=2.

Therefore, the domain is (-\infty,2)\cup(2,\infty)



8 0
3 years ago
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