Question

Pleasssseeee hellllpllllllppppp???????

Answer 1

Answer:

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

Step-by-step 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) = $\sqrt{\frac{x}{3}}$

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

∴ f(g(x)) = 3($\sqrt{\frac{x}{3}}$)²

→ Cancel the square root with power 2

∴ f(g(x)) = 3($\frac{x}{3}$)

→ 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)) = $\sqrt{\frac{3x^{2}}{3}}$

→ 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