Question

What is the inverse of the function id="TexFormula1" title="a(x) = \frac{1}{x} - 2" alt="a(x) = \frac{1}{x} - 2" align="absmiddle" class="latex-formula">

Answer 1

a(x) = 1/x - 2

or

y = 1/x - 2

Switch x and y to find the inverse function

x = 1/y - 2

1/y = x + 2

y = 1 / (x + 2)

Answer

a^-1(x) = 1 / (x + 2)

Answer 2

To find the inverse, swap the x's and y's and solve for y. Remember that a(x) represents y

y = $\frac{1}{x}$ - 2 given

x = $\frac{1}{y}$ - 2 x's and y's swapped

x + 2 = $\frac{1}{y}$ added 2 to both sides

y(x + 2) = 1 multiplied y on both sides

y = $\frac{1}{x + 2}$ divided (x + 2) on both sides

Answer: $a^{-1} (x)$ = $\frac{1}{x + 2}$