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14 votes
14 votes
Let f(x) = 5x + 12. Find f^−1(x).

User Tim Clemans
by
2.9k points

2 Answers

16 votes
16 votes

Answer:


f^(-1)(x)=(x-12)/(5)

Explanation:

Given:


f(x)=5x+12

Replace f(x) with y:


y=5x+12

Switch variables and solve for y:


x=5y+12


x-12=5y


(x-12)/(5)=y

Simplify:


(1)/(5)x-(12)/(5)=y

Replace y with f^-1(x):


f^(-1)(x)=(1)/(5)x-(12)/(5)

Therefore, the inverse function for
f(x)=5x+12 is
f^(-1)(x)=(1)/(5)x-(12)/(5).

Notice how in the graph attached of the inverse functions that they are symmetric about the line y=x. This is a crucial characteristic of inverse functions.

Let f(x) = 5x + 12. Find f^−1(x).-example-1
User EJ Mak
by
3.1k points
11 votes
11 votes

Answer:


\huge\boxed{f^(-1)(x)=(1)/(5)x-3}

Explanation:


f(x)=5x+15\to y=5x+15\\\\\text{exchange x to y and vice versa}\\\\x=5y+15\\\\\text{solve for}\ y\\\\5y+15=x\qquad|\text{subtract 15 from both sides}\\\\5y=x-15\qquad|\text{divide both sides by 5}\\\\y=(1)/(5)x-3

User Cvshepherd
by
2.7k points