Verified answer

Given function --

=> f(x) = 3 - 2 x . Let us find inverse of the given function.

Step 1

Write the given function as an equation --

=> y = 3 - 2 x

Step 2

Solve for x ---

=> x = ( 3 - y ) / 2

Step 3

Now write f⁻¹ (y) = ( 3 - y ) / 2

=> f⁻¹ (x) = ( 3 - x ) / 2 ................. Required inverse function.

Hence f⁻¹ (0) = ( 3 - 0 ) / 2

=> f⁻¹ (0) = ( 3 - 0 ) / 2 = 3/2 .............. Answer Answer

......................................................

Problem 2 --

=> 2 sin² x - 3 sin x - 2 = 0

This is a quadratic eqn. in sin x --

=> 2 sin² x - 3 sin x - 2 = 0

=> 2 sin² x - 4 sin x + sin x - 2 = 0

=> 2 sin x ( sin x - 2 ) + ( sin x - 2 ) = 0

=> ( 2 sin x + 1 ) ( sin x - 2 ) = 0

=> sin x = -- 1/2 Or sin x = 2 . But sin x cannot be equal to 2.

Hence acceptable value of sin x = -- 1/2

According to the given condition x lies in Third or/ and fourth quadrant. Hence --

=> x = ( 7/6 ) π Or ( 11/6 ) π .................. Answer Answer

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

.