Find F(x) such that F(1) = 2 and F'(x) = 1/x. exact answer. Thank u?

Question

I think f' means derivative rite? if it is then if we integrate to get f(x) it is Ln(x) which again doesn't satisfy the F(1) = 2. Help please. Thanxx. The 1st question is wrong. I think its F(derivative) instead of inverse

Answer 1

You forgot the constant:

f'(x) = 1/x
... implies that:
f(x) = ln(x) + C

Given f(1) = 2:

f(x) = ln(x) + C
2 = ln(1) + C
2 = 0 + C
2 = C

Now that you know C, you have the original equation:

f(x) = ln(x) + 2

Answer 2

Hey there!

Here's the answer.

F'(x)=1/x --> Write the problem.
F(x)=∫1/x dx --> Take the integral on both sides of the equation.
F(x)=ln|x|+C --> Use the formula ∫1/x dx=ln|x|+C.
F(1)=ln|1|+C --> Substitute 1 for x.
2=ln|1|+C --> Since F(1)=2, replace F(1) with 2.
2=0+C --> Use the formula ln|1|=0.
2=C --> Add 0 and C.
C=2 Use symmetric property of equality, i.e. if a=b, then b=a.
F(x)=ln|x|+C --> Write the function equation.
F(x)=ln|x|+2 Substitute 2 for C.

So the answer is F(x)=ln|x|+2.

Hope it helps!