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) = (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

Explanation:

Checking A.

`f(x) = (5)/(x) -2`

`g(x) = (x+2)/(5)`

`f(g(x)) = f((x+2)/(5) ) = (5)/((x+2)/(5) ) -2`

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

Checking B.

`f(x) = 7x-2`

`g(x) = (x+2)/(7)`

`f(g(x)) = f((x+2)/(7) ) = 7((x+2)/(7)) - 2 = x+2-2 = x`

`g(f(x)) = g(7x-2) = (7x-2 + 2)/(7) = (7x)/(7) = x`

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