Question

Plz I can’t do this

Answer 1

Answer: f(g(x))=x and g(f(x)) = x

f⁻¹(x) = g(x) YES ARE INVERSES

f⁻¹(x) ≠ g(x) NOT INVERSES

Explanation:

Inverse is when you swap the x's and y's and then solve for y.

If f⁻¹(x) = g(x), then they are inverses of each other.

Similarly, if g⁻¹(x) = f(x), they are inverses of each other.

NOTE: You can also use composition to determine if they are inverses --> If (fog)(x) = x, then they are inverses of each other.

`f(x) = (1)/(x+4)-9\\\\\\\text{Swap the x's and y's. NOTE: f(x) is y}\\x=(1)/(y+4)-9\\\\\\\text{Add 9 to both sides}\\x+9=(1)/(y+4)\\\\\\\text{Flip the fractions}\\(1)/(x+9)=y+4\\\\\\\text{Subtract 4 from both sides}\\(1)/(x+9)-4=y\\\\\\\boxed{f^(-1)(x)=g(x)\text{ so f(x) and g(x) are inverses of each other}}`

`f(x) = 3x+27\\\\\\\text{Swap the x's and y's NOTE f(x) is y}\\x=3y+27\\\\\\\text{Subtract 27 from both sides}\\x-27=3y\\\\\\\text{Divide everything by 3}\\(1)/(3)x-(27)/(3)=y\\\\\\\text{Simplify}\\(1)/(3)x-9=y\\\\\\\boxed{f^(-1)(x)\\eq g(x)\text{ so f(x) and g(x) are NOT inverses of each other}}`