Question

If e^f(x)=1+x^2, then f(x)=

Answer 1

Explanation:

point dene ke liye sukriya tumhara dost

Answer 2

`\displaystyle f(x) = \ln\left( 1 + x^2\right)`

Explanation:

We are given that:

`\displaystyle e^(f(x)) = 1 + x^2`

And we want to find f(x).

We can take the natural log of both sides:

`\displaystyle \ln\left(e^(f(x))\right) = \ln\left( 1 + x^2\right)`

Recall that ln(aᵇ) = bln(a). Hence:

`\displaystyle f(x) \ln(e) = \ln\left ( 1 + x^2\right)`

By definition ln(e) = 1. Therefore:

`\displaystyle f(x) = \ln\left( 1 + x^2\right)`