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kakasveta [241]
3 years ago
15

Which of the following pairs of functions are inverses of each other?

Mathematics
2 answers:
natta225 [31]3 years ago
6 0

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.

inn [45]3 years ago
6 0

Answer:

D.f(x)=8x³+6 and g(x)=³x-6/8

Step-by-step explanation:

apex

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1

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