Question

Let f(x)=7x-13. Find f^-1(x).
Let f(x)=x^2-16. Find f^-1(x).

Answer 1

Let f(x) = y and g(y) = x
that is g is inverse function of f

7x - 13 = y
7x = y + 13
x = (y + 13) / 7
g (y) = (y + 13) / 7
g (x) = (x + 13) / 7
hope this helps

Answer 2

1 )
f ( x ) = 7 x - 13
y = 7 x - 13
- 7 x = - y - 13 / *( -1 )
7 x = y + 13
x = ( y + 13 ) / 7
f^-1( x ) = ( x + 13 ) / 7
2 )
f ( x ) = x² - 16
y = x² - 16
- x² = - y - 16 /*(-1 )
x² = y + 16

`x= \sqrt{ y^(2) +16} \\ f ^(-1)(x) = \sqrt{ x^(2) +16}`