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2 months ago

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

Mathematics

2 answers:

PIT_PIT [12.4K]2 months ago

6 0

Answer:

D. The functions f(x)=8x³+6 and g(x)=³√(x-6)/8 are inverses of each other.

Explanation:

apex

babunello [11.8K]2 months ago

6 0

Answer:

The correct pair of inverse functions is:

Option: C

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

Detailed explanation:

Two functions, f(x) and g(x), are inverses if:

f(g(x)) = g(f(x)) = x

which means the composition of the two functions results in the identity function regardless of the order.

Given $f(x)=\dfrac{x}{12}+15$ and $g(x)=12x-15$ , compute f(g(x)):

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

Thus, option A is incorrect.

Given $f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}$ , compute f(g(x)):

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

Thus, option B is incorrect.

Given $f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3$ , compute f(g(x)):

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

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

Thus, option D is incorrect.

Given $f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}$ , compute f(g(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, compute g(f(x)):

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

Hence, option C is correct.

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