Question

Help answer all please wrong answers will get reported

Answer 1

If
`f^(-1)(x)` is the inverse of
`f(x)`, then by definition of inverse functions,

`\left(f\circ f^(-1)\right)(x) = f\left(f^(-1)(x)\right) = x`

Given
`f(x) = 2x-8`, the inverse, if its exists, satisfies the equation above. Evaluate
`f` at the inverse, we have

`f\left(f^(-1)(x)\right) = 2 f^(-1)(x) - 8 = x`

Solve for the inverse:

`2 f^(-1)(x) - 8 = x`

`2 f^(-1)(x) = x + 8`

`\boxed{f^(-1)(x) = \frac12 x + 4}`

Given
`g(x) = \frac13 x + 5`, we do the same thing as before to find its inverse.

`g\left(g^(-1)(x)\right) = \frac13 g^(-1)(x) + 5 = x \implies \boxed{g^(-1)(x) = 3x - 15}`