What is the inverse of the function y = 2x + 5y=2x+5?

1 Answer
Max
Jan 2, 2016

If f(x)=2x+5f(x)=2x+5
f(x)^-1=(x-5)/2f(x)−1=x−52

Explanation:

This method works, but I'm not sure how sound it is mathematically.

Let f(x)=yf(x)=y
so y=2x+5y=2x+5
then rearrange for xx
so x=(y-5)/2x=y−52
Now swap the subject for f(x)^-1f(x)−1 and the yy for xx.
f(x)^-1=(x-5)/2f(x)−1=x−52

You can check the answer by substituting in a value for xx, example x=3x=3

f(3)=6+5=11f(3)=6+5=11
Then put the answer of that into the inverse equation, and you should receive the first number you put in.

f(11)^-1=(11-5)/2=6/2=3f(11)−1=11−52=62=3

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