Finding a function based on the tangent line

Question

I need your help with this question:

The tangent line to the function f(x) at x=1 is y=3x-2. Find f(x) (without using integrals).

I know that the derivative at x=1 should be 3, but without more information, how am I suppose to find f(x) ? This is a multiple answers question, but at least 3 answers gives a derivative of 3 when putting x=1.

Thank you.

Answer 1

You can't find $f(x)$ because you aren't given enough information. There are many functions that share the same tangent line at a given point.

But you can find $f(1)$ because $f(1)=\ell(1)$, where $\ell$ is the function whose graph is the given tangent line (i.e., $\ell(x)=3x-2$). That's because the tangent at $x=1$ passes through the point $(1,f(1))$.

EDIT: Sorry, I didn't see that you actually do have more information that you aren't telling us.

Note that you really have both $f'(1)=\ell'(1)=3$ and $f(1)=\ell(1)=1$. You may be able to eliminate all but one of the possible answers with this.

Can you also please give us the actual answers you have to choose from?