f(2x+3)=4x+7 find the formula that defines f^-1
Answers
Answer:
f−1(x) represents the inverse of f(x). The inverse of a function “undoes” that function. Basically, the definition of an inverse is if you put a number x into f(x) and get the number y, then if you put y into the inverse you get back x.Or in a single concise mathematical statement: f−1(f(x))=x.
Recall that you can use y instead of f(x), so f(x)=4x−7 can also be written as y=4x−7. The process for finding the inverse of this function is to flip the variables—make all x’s into y's and all y’s into x's—and then solve for y. So you get:
x=4y−7
x+7=4y
y=x+74
And that’s our inverse function! Just change y to f−1(x) and now we have the final answer: f−1(x)=x+74
Playing around with this shows how this inverse function “undoes” our original function f(x). Think of what f(x) does—it multiplies x by 4 and then subtracts 7. So our inverse f−1 adds 7 and then divides by 4. Or mathematically, if we take x and apply f to it, we get f(x)=4x−7. Then if we take 4x−7 and apply f−1 to it, we get f−1(4x−7)=4x−7+74=4x4=x. So just like that our inverse function has undone f(x).
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