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What is the inverse of the function {:[f(x)=-(1)/(2)(x+3)?],[f^(-1)(x)=]:}

What is the inverse of the function f(x)=−12(x+3) f(x) = -\frac{1}{2}(x+3) ? f−1(x)= f^{-1}(x) =

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Q. What is the inverse of the function f(x)=−12(x+3) f(x) = -\frac{1}{2}(x+3) ? f−1(x)= f^{-1}(x) =
  1. Switching roles and solving for y: To find the inverse of the function f(x)=−12(x+3)f(x) = -\frac{1}{2}(x + 3), we need to switch the roles of xx and f(x)f(x) and then solve for the new xx.\newlineLet y=f(x)y = f(x), so we have y=−12(x+3)y = -\frac{1}{2}(x + 3).\newlineNow we replace f(x)f(x) with yy and solve for xx:\newliney=−12(x+3)y = -\frac{1}{2}(x + 3)
  2. Switching xx and yy to find the inverse function: Next, we switch xx and yy to find the inverse function:\newlinex=−(12)(y+3)x = -\left(\frac{1}{2}\right)(y + 3)
  3. Solving for y to get the inverse function: Now we solve for y to get the inverse function. Start by multiplying both sides by −2-2 to get rid of the fraction:\newline−2x=y+3-2x = y + 3
  4. Writing the inverse function: Next, subtract 33 from both sides to isolate yy:\newline−2x−3=y-2x - 3 = y
  5. Writing the inverse function: Next, subtract 33 from both sides to isolate yy:\newline−2x−3=y-2x - 3 = yFinally, we write the inverse function with yy replaced by f−1(x)f^{-1}(x):\newlinef−1(x)=−2x−3f^{-1}(x) = -2x - 3

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