Question

1) Property of inverse functions If f(x): (-1,4 ] → [3,7) → this means f(x) is a function with domain (-1,4 ) and range (3,7] And f(x) is known to have an inverse function; f(x) Find the domain and range of f(x) f-1(x): HINT: x by y's 2. Inverse functions of well known functions – find the inverse function-use proper notation - an inverse function is not a single sided express if f(x) =x, the inverse function is not x (x is just an expression / not a function) a) f(x) = 7* → b) f(x) = log2 (x) → c) f(x) = x? if x< 0 → d) f(x) = x 3. Draw the graph that correspond to the following relations (they may also be functions) a) f(x) = sinx b) * = cos y +
answer all please!

Answer 1

2 Range of f que [Let ► fl): 1-1,4] → [3,7] Domain of f = Range of par = [1,4] Domain of p- [3,7] f'(x) : [3,7) → [-1,4] R>a) f (92) = 72 => y= af eny = xlnt 27 x = liny en sy a = lnzy {"ly) - Ingy [:' y=f(x) => x=f"(] =7f-96) - Inga by f(x) = log2 (3) y=f60] >> y = logo, co [let y=f(2] X=129 >> f-'(y) = 12 cleo [:' y=f(2) => x =f“()] => f'(X) = 122 c> f(x) = x² if x<0. > y = x2 [Let y = f(od 27- Vy - x [since x is negative] => f'(x) =- ["y=f(x)=> 2=f(y)] => 14-16) 2-55 where x>0.

3 dy f(x)=n >> y = 23 [Let y=f(x)] y' >> f-'ly)2 y's since, x = f'(y)] >>4-() 27 23 20 37a) f(x) = sinx by se z cesy AY an →

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