QuestionFind the inverse function for .
Studdy Solution
STEP 1
Assumptions1. The function is defined as for . . We need to find the inverse function .
STEP 2
To find the inverse function, we first replace with to get the equation in terms of and .
STEP 3
The next step to find the inverse function is to swap and . This gives us an equation in terms of .
STEP 4
Next, we need to solve this equation for . Start by taking the reciprocal of both sides to get rid of the exponent of -1.
STEP 5
Subtract1 from both sides to isolate on one side of the equation.
STEP 6
Finally, take the eighth root of both sides to solve for .
STEP 7
Now that we have solved for , we can replace with to express our answer as the inverse function.
The inverse function of is .
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