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Find the inverse function in slope-intercept form (mx+b) : f(x)=-(3)/(2)x+9 Answer: f^(-1)(x)=

Find the inverse function in slope-intercept form (mx+b) (\mathrm{mx}+\mathrm{b}) :\newlinef(x)=−32x+9 f(x)=-\frac{3}{2} x+9 \newlineAnswer: f−1(x)= f^{-1}(x)=

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Full solution

Q. Find the inverse function in slope-intercept form (mx+b) (\mathrm{mx}+\mathrm{b}) :\newlinef(x)=−32x+9 f(x)=-\frac{3}{2} x+9 \newlineAnswer: f−1(x)= f^{-1}(x)=
  1. Replace with yy: To find the inverse function, we first replace f(x)f(x) with yy to make the equation easier to work with.\newliney=−(32)x+9y = -\left(\frac{3}{2}\right)x + 9
  2. Swap x and y: Next, we swap x and y to find the inverse function. This means we replace yy with xx and xx with yy in the equation.x=−(32)y+9x = -\left(\frac{3}{2}\right)y + 9
  3. Solve for y: Now, we need to solve for y to get the inverse function in slope-intercept form y=mx+by = mx + b. First, we'll move the term involving yy to one side and the constant to the other side.\newline32y=−x+9\frac{3}{2}y = -x + 9
  4. Isolate y: To isolate y, we divide both sides of the equation by (32)(\frac{3}{2}), which is the same as multiplying by the reciprocal, 23\frac{2}{3}.\newliney=(−23)x+(23)⋅9y = \left(-\frac{2}{3}\right)x + \left(\frac{2}{3}\right)\cdot 9
  5. Simplify constant term: Simplify the constant term (23)⋅9(\frac{2}{3})\cdot 9 to get the final inverse function.y=(−23)x+6y = \left(-\frac{2}{3}\right)x + 6

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