Question

What is the inverse of the logarithmic function
f(x) = log2x?
f –1(x) = x2

f –1(x) = 2x

f –1(x) = logx2

f –1(x) = 1/log2x

Answer 1

Answer:

$f^{-1}(x)=2^x$

B is the correct option.

Step-by-step explanation:

We have to find the inverse of the logarithmic function $f(x)=\log_2x$

Below are the steps to find the inverse:-

Step 1:-

Set f(x) =y

$y=\log_2x$

Step 2:-

Interchange x and y

$x=\log_2y$

Step 3:-

Solve for y

We know the relation:-

If $y=b^x\Rightarrow x=\log_b(y)$

Using this relation, we have

b=2

$y=2^x$

Step 3:-

The value of y is the inverse of the function.

$f^{-1}(x)=2^x$

B is the correct option.

Answer 2

Answer:

b

Step-by-step explanation: