hmic functions question 9, 5.4.75 part 5 of 8 hw score: 46.67%, 7 of 15 points points: 0 of 1 use the given…

hmic functions question 9, 5.4.75 part 5 of 8 hw score: 46.67%, 7 of 15 points points: 0 of 1 use the given function f to answer parts (a) through (f) below. f(x)=ln(x + 6) (c) from the graph, determine the range and any asymptotes of f. the range of f is (-∞,∞). (type your answer in interval notation.) determine the vertical asymptote of f. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the vertical asymptote of f is x = -6. (simplify your answer.) b. there is no vertical asymptote. (d) find f⁻¹, the inverse of f. f⁻¹(x)= (simplify your answer.) example get more help
Answer
Explanation:
Step1: Recall the method to find inverse
Set (y = f(x)=\ln(x + 6)).
Step2: Swap (x) and (y)
We get (x=\ln(y + 6)).
Step3: Solve for (y)
Exponentiate both sides using the base - (e). Since (x=\ln(y + 6)), then (e^{x}=y + 6).
Step4: Isolate (y)
Subtract 6 from both sides: (y=e^{x}-6). So (f^{-1}(x)=e^{x}-6).
Answer:
(e^{x}-6)