Question

Which function is the inverse of f(x) = 2x+3?

or(x) = -x-
F(x) = x -
r1(x) = –2x+3
or(x) = 2x + 3

Answer 1

The inverse of the function
`f\left( x \right) = 2x + 3\ is\ {f^( - 1)}\left( x \right) = \frac{{x - 3}}{2}}`

Solution:

Given function is:

f(x) = 2x + 3

We have to find the inverse of f(x)

The inverse of a function is writing x in terms of y

Let,

y = f(x)

Then,

y = 2x + 3

Exchanges the variables x for y and y for x

`x = 2y + 3`

Isolate the variable y, which means keep "y" alone in left side of equation

`2y+3 = x\\\\2y = x - 3\\\\y = (x-3)/(2)`

Therefore, inverse of function is:

`f^(-1)(x)= \frac{{x - 3}}{2}`