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Find the inverse function of the function 
f(x)=2x-7.

f^(-1)(x)=(x+7)/(2)

f^(-1)(x)=(x-2)/(7)

f^(-1)(x)=(x+2)/(7)

f^(-1)(x)=(x-7)/(2)

Find the inverse function of the function f(x)=2x7 f(x)=2 x-7 .\newlinef1(x)=x+72 f^{-1}(x)=\frac{x+7}{2} \newlinef1(x)=x27 f^{-1}(x)=\frac{x-2}{7} \newlinef1(x)=x+27 f^{-1}(x)=\frac{x+2}{7} \newlinef1(x)=x72 f^{-1}(x)=\frac{x-7}{2}

Full solution

Q. Find the inverse function of the function f(x)=2x7 f(x)=2 x-7 .\newlinef1(x)=x+72 f^{-1}(x)=\frac{x+7}{2} \newlinef1(x)=x27 f^{-1}(x)=\frac{x-2}{7} \newlinef1(x)=x+27 f^{-1}(x)=\frac{x+2}{7} \newlinef1(x)=x72 f^{-1}(x)=\frac{x-7}{2}
  1. Replace with yy: To find the inverse function, we first replace f(x)f(x) with yy:y=2x7y = 2x - 7
  2. Swap x and y: Next, we swap x and y to solve for the new y, which will be the inverse function:\newlinex=2y7x = 2y - 7
  3. Solve for new y: Now, we solve for yy by adding 77 to both sides of the equation: x+7=2yx + 7 = 2y
  4. Isolate y: Finally, we divide both sides by 22 to isolate yy:y=x+72y = \frac{x + 7}{2}This is the inverse function, denoted as f1(x)f^{-1}(x).

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