Find the inverse function of $$ f(x)=e^{3 x+5}-4 $$. $$ f^{-1}(x)= $$ Write "log_b(a)" for $$ \log _{b}(a) $$ or $$ " \ln (a) $$ " for $$ \ln (a) $$.

Question

UpStudy AI · Accepted Answer

To find the inverse function, start with:

y = e^(3x + 5) - 4

Step 1: Add 4 to both sides:
  y + 4 = e^(3x + 5)

Step 2: Take the natural logarithm of both sides:
  ln(y + 4) = 3x + 5

Step 3: Solve for x:
  x = [ln(y + 4) - 5] / 3

Step 4: Replace y with x to write the inverse function:
  f^(-1)(x) = [ln(x + 4) - 5] / 3

Thus, the inverse function is:
  f^(-1)(x) = (ln(x + 4) - 5) / 3
The inverse function is $$ f^{-1}(x) = \frac{\ln(x + 4) - 5}{3} $$.

Find the inverse function of .

Write “log_b(a)” for or " for .