How do you find the inverse of $f (x) = 5 x + 10$ $f(x)= 5x + 10$ ?

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Answer 1 · 2016-02-14T16:40:56

The inverse of a function is the relation that is formed when the function is transformed over the line $y = x$ $y = x$

The inverse can be found algebraically by switching x for y and y for x in the equation. You must then isolate y.

$f (x) = 5 x + 10$ $f(x) = 5x + 10$

$y = 5 x + 10$ $y = 5x + 10$

$x = 5 y + 10$ $x = 5y + 10$

$x - 10 = 5 y$ $x - 10 = 5y$

$\frac{x - 10}{5} = y$ $(x - 10)/5 = y$

So, $f^{- 1} (x) = \frac{x - 10}{5}$ $f^-1(x) = (x - 10)/5$

Practice exercises:

a) $f (x) = 3 x + 4$ $f(x) = 3x + 4$

b) $g (x) = \sqrt{4 x - 1}$ $g(x) = sqrt(4x - 1)$

c) $h (x) = \frac{2}{2 x - 3}$ $h(x) = 2/(2x - 3)$

Good luck!

How do you find the inverse of f(x)=5x+10f(x)= 5x + 10?