Let f be the function from R to R defined by f(x)=x2. Find f−1(1)

Question

Let f be the function from R to R defined by f(x)=x2. Find  f−1(1)

joshyoung05M · Accepted Answer

Given:&amp;nbsp;f:R→Rf(x)=x2f−1(1)&amp;nbsp;contains every component of R that has image 1 as its.f(x)=1Since&amp;nbsp;f(x)=x2, we have:x2=1x2−1=0(x+1)(x−1)=0These are the equation&#039;s solutions:&amp;nbsp;x=1&amp;nbsp;and&amp;nbsp;x=−1&amp;nbsp;and&amp;nbsp;f−1(1)&amp;nbsp;thus contains&amp;nbsp;−1&amp;nbsp;ad&amp;nbsp;1.f−1(1)={−1,1}

Nick Camelot · Accepted Answer

Let f be the function from ℝ to ℝ defined by f(x)=x2. We need to find f−1(1).To find the inverse of f, we set y=f(x) and solve for x. So, we have:y=x2To find x, we take the square root of both sides:y=x2y=|x|Since f is a real-valued function, f−1 will also be a real-valued function. Therefore, we consider only the positive square root:y=xNow, we substitute y=1 to find x:1=xx=1Thus, f−1(1)=1.

Mr Solver · Accepted Answer

To solve the equation f−1(1) for the function f(x)=x2, we need to find the inverse of f(x) and evaluate it at 1.To find the inverse of f(x), we switch the roles of x and f(x) and solve for x. So, we start with the equation y=x2 and rearrange it as follows:y=x2y=x2y=|x|Here, we take the square root of both sides and introduce the absolute value to account for the positive and negative roots.Now, to find f−1(1), we substitute 1 for y:1=|x|Since the square root of 1 is 1, we have:1=|x|To solve for x, we consider the two cases for the absolute value:Case 1: |x|=xIn this case, we have 1=x.Case 2: |x|=−xIn this case, we have 1=−x. Solving for x, we get x=−1.Therefore, the solutions to f−1(1) are x=1 and x=−1.

madeleinejames20 · Accepted Answer

Result:1Solution:First, let&#039;s find the inverse function f−1(x) by swapping the variables x and y and solving for y:x=y2x=yTherefore, the inverse function is given by f−1(x)=x.Now, we can find the value of f−1(1) by substituting x=1 into the inverse function:f−1(1)=1Simplifying further, we have:f−1(1)=1Hence, the value of f−1(1) is 1.

Let f be the function from R to R defined by f(x) = x^{2}. Find

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