Question

Using interval notation, determine the largest domain over which the given function is one‑to‑one. Then, provide the equation for the inverse of the function that is restricted to that domain.

If two equally large domains exist over which the given function is one‑to‑one, you may use either domain. However, be certain that the equation for the inverse function you submit is appropriate for the particular domain you choose.

f(x)=10−x

(Give your answer as an interval in the form (∗,∗).

Use the symbol ∞ for infinity, ∪ for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter ∅

if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)

x∈

(Give an exact answer. Use symbolic notation and fractions where needed.)

f−1(x)=

Answer 1

is one one in whole , that is .

and . If for we have, , then . Then . So is one one in .

. So, inverse of is in .

so in conclusion, is one one for all .

for all .