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) 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)
$\displaystyle y=3-2x \quad \Rightarrow x=\frac{(3-y)}{2} $
$\displaystyle \ f^{-1} (y) = \frac{(3-y)}{2} \quad (\because f(x)=y)$
$\displaystyle \therefore \boxed { f^{-1} (x) = \frac{(3-x)}{2}}$
to find $\displaystyle f^{-1}( 5) $ put x= 5 in above equation
2) use $\displaystyle x^4-y^4=(x^2+y^2) \cdot (x^2-y^2)$2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?
(because $\displaystyle a^2-b^2=(a+b)(a-b)$