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

b

Explanation:

Answer 2

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

B is the correct option.

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.