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Andrej [43]
3 years ago
15

Which pair of functions are inverses of each other?

Mathematics
1 answer:
AlladinOne [14]3 years ago
5 0

Answer:

The only pair of functions that are inverses of each other are the ones for option D.

Step-by-step explanation:

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

f( g(x) ) = x

g( f(x) ) = x

So we need to check that with all the given options.

A)

f(x) = \frac{x}{7} + 10 \\g(x) = 7*x - 10\\

then:

f(g(x)) = \frac{7*x + 10}{7} -10 = x + \frac{10}{7}  - 10

This is clearly different than x, so f(x) and g(x) are not inverses.

B)

f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3

Then:

f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 }  = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}

This is different than x, so f(x) and g(x) are not inverses.

C)

f(x) = \frac{7}{x} -2 \\g(x) = \frac{x + 2}{7}

Then:

f(g(x)) = \frac{7}{\frac{x + 2}{7} } - 2 = \frac{7*7}{x + 2}  - 2

Obviously, this is different than x, so f(x) and g(x) are not inverses.

D)

f(x) = 9*x - 6\\g(x) = \frac{x + 6}{9}

Then:

f(g(x)) = 9*\frac{x + 6}{9}  - 6 = x + 6 - 6 = x\\g(f(x)) = \frac{(9*x - 6) + 6}{9}  = x

In this case we can conclude that f(x) and g(x) are inverses of each other.

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