Question

15 POINTS AND I WILL GIVE BRAINLIEST

Are f and g inverses of each other? Support your response algebraically

6. f(x) = -(1/5)x + 3/5
g(x) = -5x + 3

7. f(x) = x + 1/2
g(x) = 1x - 1/2

Answer 1

Answer:

see explanation

Step-by-step explanation:

If f(x) and g(x) are the inverse of each other then

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

6.

f(g(x) = f(- 5x + 3 )

= - $\frac{1}{5}$(- 5x + 3) + $\frac{3}{5}$

= x - $\frac{3}{5}$ + $\frac{3}{5}$ = x

g(f(x) = g(- $\frac{1}{5}$ x + $\frac{3}{5}$)

= - 5(- $\frac{1}{5}$ x + $\frac{3}{5}$)

= x - 3 + 3 = x

Since f(g(x)) = g(f(x)) = x then f(x) and g(x) are the inverse of each other

7.

f(g(x)) = f(x - $\frac{1}{2}$)

= x - $\frac{1}{2}$ + $\frac{1}{2}$ = x

g(f(x)) = g(x + $\frac{1}{2}$)

= x + $\frac{1}{2}$ - $\frac{1}{2}$ = x

Hence f(x) and g(x) are the inverse of each other