# Thread: Inverse functions, solving equations.

1. ## Inverse functions, solving equations.

1) If f (x) = 3 - 2x , calculate the value of f -1 (5) .

2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?

2. Originally Posted by sri340
1) If f (x) = 3 - 2x , calculate the value of f -1 (5) .
2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?
1)
f (x) = 3 - 2x = y(say)
$y=3-2x \quad \Rightarrow x=\frac{(3-y)}{2}$
$\ f^{-1} (y) = \frac{(3-y)}{2} \quad (\because f(x)=y)$
$\therefore \boxed { f^{-1} (x) = \frac{(3-x)}{2}}$
to find $f^{-1}( 5)$ put x= 5 in above equation

2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?
2) use $x^4-y^4=(x^2+y^2) \cdot (x^2-y^2)$
(because $a^2-b^2=(a+b)(a-b)$