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densk [106]
3 years ago
7

" title="\frac{3}{4}\alpha-1\frac{1}{5}=2\frac{3}{4}" alt="\frac{3}{4}\alpha-1\frac{1}{5}=2\frac{3}{4}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
velikii [3]3 years ago
5 0
I DONT KNOW LOL PLS STOP CHEATING
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An analyst for a new company used the first three years of revenue data to project future revenue for the company. The analyst p
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Which of the following pairs of functions are inverses of each other?
natta225 [31]

Answer:

The pair which are inverse of each other are:

Option: C

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Step-by-step explanation:

Two functions f(x) and g(x) are said to be inverse of each other if:

fog(x)=gof(x)=x

i.e. the composition of two functions give identity no matter what the order is.

A)

f(x)=\dfrac{x}{12}+15 and g(x)=12x-15

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x

Hence, option: A is incorrect.

B)

f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x

Hence, option: B is incorrect.

D)

f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)

fog(x)=9+\sqrt[3]{9-x^3}\neq x

Hence, option: D is incorrect.

C)

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})

fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x

Similarly,

gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x

Hence, option: C is the correct option.

6 0
3 years ago
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4. Find x. Then find each indicated measure.
Zigmanuir [339]

Answer:

             x=4\\\\EG=9\\\\ED=18

Step-by-step explanation:

\dfrac{x+5+9}{x+5}=\dfrac{12}{6}\\\\\dfrac{x+14}{x+5}=2\\\\x+14=2(x+5)\\\\x+14=2x+10\\\\14-10=2x-x\\\\x=4\\\\EG=4+5=9\\\\ED=9+9=18

3 0
3 years ago
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