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

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

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Answer 1 · 2016-01-02T14:43:28

If $f (x) = 2 x + 5$ $f(x)=2x+5$
${f (x)}^{- 1} = \frac{x - 5}{2}$ $f(x)^-1=(x-5)/2$

Explanation:

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

Let $f (x) = y$ $f(x)=y$
so $y = 2 x + 5$ $y=2x+5$
then rearrange for $x$ $x$
so $x = \frac{y - 5}{2}$ $x=(y-5)/2$
Now swap the subject for ${f (x)}^{- 1}$ $f(x)^-1$ and the $y$ $y$ for $x$ $x$ .
${f (x)}^{- 1} = \frac{x - 5}{2}$ $f(x)^-1=(x-5)/2$

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

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

${f (11)}^{- 1} = \frac{11 - 5}{2} = \frac{6}{2} = 3$ $f(11)^-1=(11-5)/2=6/2=3$

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

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