Q. For the function f(x)=5x7+9, find f−1(x).f−1(x)=75x−9f−1(x)=75x−9f−1(x)=57x−9f−1(x)=57x−9
Write Function: First, let's write down the function we're dealing with: f(x)=5x7+9. We need to find the inverse of this function, which we'll denote as f−1(x). To do this, we'll first replace f(x) with y for simplicity: y=5x7+9.
Swap x and y: Now, we'll swap x and y to start finding the inverse: x=5y7+9.
Isolate y: Next, we need to isolate y on one side. So, we'll subtract 9 from both sides: x−9=5y7.
Divide by 5: Then, we divide both sides by 5 to get: (x−9)/5=y7.
Take 7th Root: Now, to solve for y, we take the 7th root of both sides: y=75x−9.
Replace y: Finally, we replace y with f−1(x) to denote the inverse function: f−1(x)=75x−9.
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