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Find the inverse function of the function 
f(x)=2x-5.

f^(-1)(x)=(x-2)/(5)

f^(-1)(x)=(x+2)/(5)

f^(-1)(x)=(x-5)/(2)

f^(-1)(x)=(x+5)/(2)

Find the inverse function of the function f(x)=2x5 f(x)=2 x-5 .\newlinef1(x)=x25 f^{-1}(x)=\frac{x-2}{5} \newlinef1(x)=x+25 f^{-1}(x)=\frac{x+2}{5} \newlinef1(x)=x52 f^{-1}(x)=\frac{x-5}{2} \newlinef1(x)=x+52 f^{-1}(x)=\frac{x+5}{2}

Full solution

Q. Find the inverse function of the function f(x)=2x5 f(x)=2 x-5 .\newlinef1(x)=x25 f^{-1}(x)=\frac{x-2}{5} \newlinef1(x)=x+25 f^{-1}(x)=\frac{x+2}{5} \newlinef1(x)=x52 f^{-1}(x)=\frac{x-5}{2} \newlinef1(x)=x+52 f^{-1}(x)=\frac{x+5}{2}
  1. Replace with yy: To find the inverse function, we first replace f(x)f(x) with yy:y=2x5y = 2x - 5
  2. Swap x and y: Next, we swap x and y to solve for the new y, which will give us the inverse function:\newlinex=2y5x = 2y - 5
  3. Solve for new y: Now, we solve for yy by adding 55 to both sides of the equation:\newlinex+5=2yx + 5 = 2y
  4. Isolate yy: Finally, we divide both sides by 22 to isolate yy:y=x+52y = \frac{x + 5}{2}This is the inverse function of f(x)f(x).

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