Question

PLS HELP QUICKLY
Which pair of functions are inverses of each other?
5
O A. f(x) = -2 and g(x) = +2
B. f(x) = 7x-2 and g(x) = 2
C. f(x) =x/5+ 6 and g(x) = 5x - y
D. f(x) = 3+ 6 and g(x) = 6x³

Answer 1

Answer: B

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

How to solve:

check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)

f[g(x)] = x

g[f(x)] = x

Step-by-step explanation:

Checking A.

$f(x) = \frac{5}{x} -2$

$g(x) = \frac{x+2}{5}$

$f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2$

This does not equal x, so we know these are not inverses

Checking B.

$f(x) = 7x-2$

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

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

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

since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.