[20 PTS] Let f(x) = log2(2x). Which of the following is the value of d/dx(f^-1(3)) ?

Question

asked May 22, 2023 24.1k views

1 Answer

Mutantkeyboard · Answer 1 · 2023-05-27T23:04:22+0000

Answer:

D)
4*ln(2)

Explanation:

Find the inverse function of f(x):

f(x)=log_2(2x)

y=log_2(2x)

x=log_2(2y)

2^x=2y

2^(x-1)=y

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

Take the derivative of the inverse function:

(d)/(dx)(f^(-1)(x))

(d)/(dx)(2^(x-1))

(d)/(dx)(e^((x-1)(ln2))) <-- Logarithmic Differentiation

$ln(2)*e^{(x-1)(ln(2))$

ln(2)*2^(x-1)

Substitute x=3:

ln(2)*2^(3-1)

ln(2)*2^2

4*ln(2)