Question

Find the functions f(u) and g(x) for y=ln(3x² + 1) so that y=f(u) and u=g(x)

a) f(u) = ln(u), g(x) = 3x² + 1
b) f(u) = ln(u), g(x) = √(3x² + 1)
c) f(u) = ln(3u² + 1), g(x) = x
d) f(u) = ln(u² + 1), g(x) = 3x

Answer 1

To find the functions f(u) and g(x) for y=ln(3x² + 1) so that y=f(u) and u=g(x), we need to isolate the variable inside the logarithm and rearrange the equation. The functions f(u) = ln(u) and g(x) = sqrt((e^x - 1)/3) can be used.

Step-by-step explanation:

To find the functions f(u) and g(x) for y=ln(3x² + 1) so that y=f(u) and u=g(x), we need to isolate the variable inside the logarithm.

To do this, we can rearrange the equation as follows:

3x² + 1 = e^y

Now, let's solve for x²:

x² = (e^y - 1)/3

Next, take the square root of both sides:

x = sqrt((e^y - 1)/3)

Therefore, we can write the functions as f(u) = ln(u) and g(x) = sqrt((e^x - 1)/3).