The equation of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x)=\frac{1}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
How to find the inverse of a function:
- First, replace f(x) with y
- Replace every x with a y and replace every y with an x
- Solve the equation from Step 2 for y
- Replace y with [tex]f^{-1}(x)[/tex]
∵ f(x) = 2x - 7
- Replace f(x) by y
∴ y = 2x - 7
- Replace x by y and y by x
∴ x = 2y - 7
- Let us solve to find y
- Add 7 to both sides
∴ x + 7 = 2y
- Divide each term in two sides by 2
∴ [tex]\frac{x}{2}+\frac{7}{2}=y[/tex]
- Switch the two sides
∴ [tex]y=\frac{x}{2}+\frac{7}{2}[/tex]
- Write [tex]\frac{x}{2}[/tex] as [tex]\frac{1}{2}x[/tex]
∴ [tex]y=\frac{1}{2}x+\frac{7}{2}[/tex]
- Replace y by [tex]f^{-1}(x)[/tex]
∴ [tex]f^{-1}(x)=\frac{1}{2}x+\frac{7}{2}[/tex]
The equation of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x)=\frac{1}{2}x+\frac{7}{2}[/tex]
Learn more:
You can learn more about the inverse function in brainly.com/question/1632445
#LearnwithBrainly
