Worth 20 points which functions are equivalent to f(x)= 4√162? check all that apply a)f(x)= 162 x/4 b)f(x)=(3 4√2)x c)f(x)=9 4√2 x d)f(x)=162 4/x e)f(x)=[3 (2 1/4)]x

The options that are equivalent to the given function are;

Option A

Option B

Option E

The correct options are;

A) f(x) =

B) f(x) = (3∜2

C) f(x) =

D) f(x) =

E) f(x) =

We are given the function; f(x) =

Now, when we have something like;

This expression can also be expressed as;

Therefore our function can also be expressed as; f(x) =

Option A; This is correct because it is equal to our function gotten

Option B; f(x) = (3∜2

From earlier, we will have;  (3 ×

Now, 3 can also be expressed as

Thus, we now have;

( ×

Factorizing out the 1/4 exponent gives;

(81 × 2

⇒ =

This is same with our function and it is correct

Option C; f(x) = (9∜2

This is similar to our equation in option B which was correct but the difference here is 9 instead of 3 and clearly this option is not correct.

Option D; f(x) =

This is not the same with our function and so it is wrong

Option E; f(x) =

As seen in option B;

3 can also be expressed as

Thus, we now have;

;( ×

Factorizing out the 1/4 exponent gives;

(81 × 2

⇒ =

This is same with our function and it is correct

Read more at; link

b

step-by-step explanation: