Question

Pleasssseeee hellllpllllllppppp???????

Answer 1

f(x) and g(x) are inverse functions

Explanation:

In the two functions f(x) and g(x) if, f(g(x)) = g(f(x)) = x, then

f(x) and g(x) are inverse functions

Let us use this rule to solve the question

∵ f(x) = 3x²

∵ g(x) =
`\sqrt{(x)/(3)}`

→ Find f(g(x)) by substitute x in f(x) by g(x)

∴ f(g(x)) = 3(
`\sqrt{(x)/(3)}`)²

→ Cancel the square root with power 2

∴ f(g(x)) = 3(
`(x)/(3)`)

→ Cancel the 3 up with the 3 down

∴ f(g(x)) = x

→ Find g(f(x)) by substitute x in g(x) by f(x)

∴ g(f(x)) =
`\sqrt{(3x^(2))/(3)}`

→ Cancel the 3 up with the 3 down

∴ g(f(x)) =
`\sqrt{x^(2)}`

→ Cancel the square root with power 2

∴ g(f(x)) = x

∵ f(g(x)) = g(f(x)) = x

→ By using the rule above

∴ f(x) and g(x) are inverse functions